{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[558,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0001","image_path":"images/combination_0001.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0001_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0001_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0001_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0001_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0001_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[553,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0002","image_path":"images/combination_0002.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0002_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0002_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0002_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":"combination_0002_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0002_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[565,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0003","image_path":"images/combination_0003.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0003_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0003_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0003_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":"combination_0003_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0003_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":3,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0004","image_path":"images/combination_0004.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0004_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0004_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0004_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":"combination_0004_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0004_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":4,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0005","image_path":"images/combination_0005.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0005_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0005_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0005_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0005_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0005_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":5,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":5}],"canvas_size":[600,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0006","image_path":"images/combination_0006.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0006_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0006_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0006_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0006_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0006_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":6,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":9}],"canvas_size":[570,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0007","image_path":"images/combination_0007.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0007_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0007_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0007_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0007_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0007_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":7,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[564,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0008","image_path":"images/combination_0008.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0008_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0008_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0008_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0008_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0008_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":8,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[579,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0009","image_path":"images/combination_0009.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0009_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0009_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0009_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":"combination_0009_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0009_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":9,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0010","image_path":"images/combination_0010.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0010_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0010_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0010_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0010_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0010_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":10,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0011","image_path":"images/combination_0011.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0011_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0011_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0011_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":"combination_0011_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0011_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":11,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[580,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0012","image_path":"images/combination_0012.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0012_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0012_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0012_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":"combination_0012_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0012_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":12,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[566,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0013","image_path":"images/combination_0013.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0013_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0013_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0013_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":"combination_0013_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0013_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":13,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[556,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0014","image_path":"images/combination_0014.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0014_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0014_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0014_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":"combination_0014_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0014_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":14,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[4,1],[4,2],[5,1],[6,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[563,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0015","image_path":"images/combination_0015.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0015_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0015_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0015_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":"combination_0015_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0015_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":15,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[573,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0016","image_path":"images/combination_0016.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0016_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0016_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0016_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0016_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0016_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":16,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[583,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0017","image_path":"images/combination_0017.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0017_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0017_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0017_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0017_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0017_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":17,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0018","image_path":"images/combination_0018.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0018_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0018_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0018_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0018_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0018_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":18,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3],[4,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]],"total_cell_count":10}],"canvas_size":[593,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0019","image_path":"images/combination_0019.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0019_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0019_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0019_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":"combination_0019_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0019_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":19,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7}],"canvas_size":[596,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0020","image_path":"images/combination_0020.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0020_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0020_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0020_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":"combination_0020_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0020_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":20,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0021","image_path":"images/combination_0021.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0021_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0021_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_0021_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":"combination_0021_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0021_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":21,"target_cell_count":9,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6}],"canvas_size":[558,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0022","image_path":"images/combination_0022.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0022_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0022_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0022_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":"combination_0022_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0022_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":22,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6}],"canvas_size":[599,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0023","image_path":"images/combination_0023.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0023_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0023_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0023_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0023_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0023_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":23,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[595,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0024","image_path":"images/combination_0024.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0024_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0024_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0024_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0024_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0024_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":24,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[574,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0025","image_path":"images/combination_0025.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0025_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0025_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0025_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":"combination_0025_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0025_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":25,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":7}],"canvas_size":[597,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0026","image_path":"images/combination_0026.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0026_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0026_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0026_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":"combination_0026_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0026_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":26,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[591,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0027","image_path":"images/combination_0027.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0027_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0027_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_0027_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0027_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":27,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[557,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0028","image_path":"images/combination_0028.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0028_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0028_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0028_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":"combination_0028_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0028_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":28,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0029","image_path":"images/combination_0029.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0029_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0029_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0029_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":"combination_0029_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0029_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":29,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[584,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0030","image_path":"images/combination_0030.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0030_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0030_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0030_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":"combination_0030_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0030_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":30,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[550,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0031","image_path":"images/combination_0031.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0031_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0031_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0031_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":"combination_0031_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0031_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":31,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[554,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0032","image_path":"images/combination_0032.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0032_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0032_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0032_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0032_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0032_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":32,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[586,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0033","image_path":"images/combination_0033.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0033_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0033_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_0033_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0033_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":33,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[583,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0034","image_path":"images/combination_0034.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0034_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0034_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0034_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":"combination_0034_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0034_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":34,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[585,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0035","image_path":"images/combination_0035.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0035_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0035_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0035_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0035_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0035_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":35,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[571,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0036","image_path":"images/combination_0036.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0036_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0036_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0036_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":"combination_0036_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0036_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":36,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0037","image_path":"images/combination_0037.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0037_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0037_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0037_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":"combination_0037_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0037_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":37,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[590,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0038","image_path":"images/combination_0038.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0038_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0038_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0038_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":"combination_0038_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0038_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":38,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[563,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0039","image_path":"images/combination_0039.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0039_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0039_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0039_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0039_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0039_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":39,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[579,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0040","image_path":"images/combination_0040.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0040_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0040_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0040_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0040_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0040_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":40,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[574,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0041","image_path":"images/combination_0041.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0041_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0041_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0041_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0041_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0041_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":41,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[590,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0042","image_path":"images/combination_0042.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0042_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0042_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0042_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":"combination_0042_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0042_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":42,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7}],"canvas_size":[552,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0043","image_path":"images/combination_0043.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0043_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0043_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0043_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0043_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0043_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":43,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,3],[1,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1],[1,0],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0044","image_path":"images/combination_0044.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0044_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0044_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0044_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0044_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0044_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":44,"target_cell_count":10,"target_cells":[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]],"total_cell_count":9}],"canvas_size":[567,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0045","image_path":"images/combination_0045.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0045_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0045_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0045_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":"combination_0045_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0045_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":45,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0046","image_path":"images/combination_0046.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0046_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0046_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0046_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":"combination_0046_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0046_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":46,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":9}],"canvas_size":[572,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0047","image_path":"images/combination_0047.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0047_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0047_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0047_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":"combination_0047_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0047_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":47,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":7}],"canvas_size":[585,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0048","image_path":"images/combination_0048.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0048_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0048_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0048_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0048_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0048_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":48,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0049","image_path":"images/combination_0049.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0049_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0049_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0049_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":"combination_0049_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0049_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":49,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0050","image_path":"images/combination_0050.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0050_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0050_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0050_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0050_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0050_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":50,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[565,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0051","image_path":"images/combination_0051.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0051_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0051_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0051_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0051_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0051_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":51,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[567,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0052","image_path":"images/combination_0052.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0052_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0052_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0052_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0052_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0052_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":52,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,1],[4,0],[4,1],[5,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1],[5,1],[5,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[5,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[589,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0053","image_path":"images/combination_0053.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0053_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0053_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0053_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0053_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0053_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":53,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0054","image_path":"images/combination_0054.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0054_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0054_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0054_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":"combination_0054_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0054_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":54,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_0055","image_path":"images/combination_0055.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0055_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0055_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0055_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":"combination_0055_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0055_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":55,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[585,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0056","image_path":"images/combination_0056.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0056_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0056_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0056_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0056_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0056_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":56,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[552,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0057","image_path":"images/combination_0057.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0057_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0057_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_0057_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0057_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":57,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[587,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0058","image_path":"images/combination_0058.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0058_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0058_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0058_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0058_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0058_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":58,"target_cell_count":7,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[564,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0059","image_path":"images/combination_0059.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0059_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0059_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0059_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":"combination_0059_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0059_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":59,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[4,1],[4,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[569,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0060","image_path":"images/combination_0060.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0060_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0060_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0060_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0060_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0060_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":60,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[581,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0061","image_path":"images/combination_0061.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0061_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0061_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0061_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0061_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0061_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":61,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[586,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0062","image_path":"images/combination_0062.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0062_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0062_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0062_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0062_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0062_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":62,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[578,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0063","image_path":"images/combination_0063.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0063_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0063_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0063_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0063_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0063_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":63,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10}],"canvas_size":[580,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0064","image_path":"images/combination_0064.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0064_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0064_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0064_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":"combination_0064_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0064_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":64,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[576,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0065","image_path":"images/combination_0065.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0065_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0065_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0065_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":"combination_0065_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0065_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":65,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":9}],"canvas_size":[554,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0066","image_path":"images/combination_0066.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0066_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0066_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0066_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0066_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0066_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":66,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0067","image_path":"images/combination_0067.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0067_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0067_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0067_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0067_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0067_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":67,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"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],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0068","image_path":"images/combination_0068.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0068_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0068_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0068_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":"combination_0068_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0068_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":68,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0069","image_path":"images/combination_0069.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0069_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0069_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0069_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0069_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0069_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":69,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[557,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0070","image_path":"images/combination_0070.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0070_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0070_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0070_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0070_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0070_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":70,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[570,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0071","image_path":"images/combination_0071.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0071_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0071_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_0071_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0071_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":71,"target_cell_count":10,"target_cells":[[0,0],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4],[1,5]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[554,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0072","image_path":"images/combination_0072.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0072_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0072_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0072_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0072_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0072_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":72,"target_cell_count":10,"target_cells":[[0,0],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[567,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0073","image_path":"images/combination_0073.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0073_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0073_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0073_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0073_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0073_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":73,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0074","image_path":"images/combination_0074.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0074_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0074_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0074_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":"combination_0074_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0074_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":74,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0075","image_path":"images/combination_0075.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0075_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0075_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0075_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0075_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0075_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":75,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,1],[3,2],[3,3],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[4,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1],[4,2]]],"total_cell_count":9}],"canvas_size":[573,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0076","image_path":"images/combination_0076.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0076_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0076_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0076_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":"combination_0076_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0076_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":76,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[566,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0077","image_path":"images/combination_0077.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0077_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0077_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0077_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":"combination_0077_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0077_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":77,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0078","image_path":"images/combination_0078.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0078_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0078_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0078_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0078_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0078_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":78,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[559,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0079","image_path":"images/combination_0079.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0079_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0079_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0079_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":"combination_0079_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0079_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":79,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[567,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0080","image_path":"images/combination_0080.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0080_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0080_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0080_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":"combination_0080_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0080_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":80,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_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],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[582,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0081","image_path":"images/combination_0081.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0081_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0081_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0081_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0081_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0081_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":81,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[559,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0082","image_path":"images/combination_0082.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0082_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0082_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0082_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0082_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0082_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":82,"target_cell_count":9,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[581,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0083","image_path":"images/combination_0083.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0083_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0083_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0083_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0083_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0083_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":83,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0084","image_path":"images/combination_0084.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0084_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0084_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0084_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":"combination_0084_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0084_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":84,"target_cell_count":6,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[562,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0085","image_path":"images/combination_0085.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0085_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0085_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0085_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0085_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0085_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":85,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0086","image_path":"images/combination_0086.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0086_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0086_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0086_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":"combination_0086_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0086_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":86,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[559,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0087","image_path":"images/combination_0087.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0087_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0087_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0087_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":"combination_0087_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0087_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":87,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]],"total_cell_count":8}],"canvas_size":[575,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0088","image_path":"images/combination_0088.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0088_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0088_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0088_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0088_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0088_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":88,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[555,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0089","image_path":"images/combination_0089.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0089_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0089_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0089_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":"combination_0089_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0089_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":89,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[563,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0090","image_path":"images/combination_0090.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0090_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0090_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0090_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0090_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0090_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":90,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[555,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0091","image_path":"images/combination_0091.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0091_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0091_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0091_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0091_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0091_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":91,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":10}],"canvas_size":[576,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0092","image_path":"images/combination_0092.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0092_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0092_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0092_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0092_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0092_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":92,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0093","image_path":"images/combination_0093.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0093_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0093_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0093_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0093_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0093_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":93,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0094","image_path":"images/combination_0094.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0094_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0094_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0094_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":"combination_0094_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0094_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":94,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[598,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0095","image_path":"images/combination_0095.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0095_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0095_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0095_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0095_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0095_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":95,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2],[3,3],[3,4],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[573,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0096","image_path":"images/combination_0096.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0096_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0096_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0096_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0096_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0096_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":96,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[562,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0097","image_path":"images/combination_0097.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0097_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0097_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0097_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":"combination_0097_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0097_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":97,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[572,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0098","image_path":"images/combination_0098.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0098_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0098_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0098_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":"combination_0098_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0098_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":98,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[575,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0099","image_path":"images/combination_0099.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0099_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0099_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0099_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":"combination_0099_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0099_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":99,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[559,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0100","image_path":"images/combination_0100.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0100_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0100_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0100_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0100_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0100_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":100,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,3],[2,4]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[587,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0101","image_path":"images/combination_0101.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0101_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0101_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0101_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0101_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0101_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":101,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[559,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0102","image_path":"images/combination_0102.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0102_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0102_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0102_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":"combination_0102_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0102_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":102,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[595,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0103","image_path":"images/combination_0103.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0103_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0103_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0103_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0103_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0103_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":103,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[551,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0104","image_path":"images/combination_0104.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0104_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0104_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0104_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":"combination_0104_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0104_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":104,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[587,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0105","image_path":"images/combination_0105.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0105_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0105_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0105_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":"combination_0105_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0105_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":105,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[595,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0106","image_path":"images/combination_0106.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0106_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0106_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0106_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":"combination_0106_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0106_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":106,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":10}],"canvas_size":[565,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0107","image_path":"images/combination_0107.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0107_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0107_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0107_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0107_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0107_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":107,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[558,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0108","image_path":"images/combination_0108.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0108_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0108_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0108_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":"combination_0108_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0108_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":108,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[567,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0109","image_path":"images/combination_0109.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0109_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0109_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0109_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":"combination_0109_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0109_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":109,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[574,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0110","image_path":"images/combination_0110.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0110_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0110_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0110_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":"combination_0110_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0110_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":110,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2],[4,1],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,1],[2,2],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0111","image_path":"images/combination_0111.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0111_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0111_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0111_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":"combination_0111_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0111_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":111,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[580,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0112","image_path":"images/combination_0112.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0112_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0112_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0112_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0112_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0112_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":112,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0113","image_path":"images/combination_0113.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0113_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0113_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0113_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0113_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0113_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":113,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0114","image_path":"images/combination_0114.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0114_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0114_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0114_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":"combination_0114_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0114_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":114,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6}],"canvas_size":[568,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0115","image_path":"images/combination_0115.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0115_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0115_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0115_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":"combination_0115_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0115_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":115,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0116","image_path":"images/combination_0116.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0116_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0116_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0116_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0116_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0116_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":116,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[565,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0117","image_path":"images/combination_0117.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0117_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0117_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0117_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":"combination_0117_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0117_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":117,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[595,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0118","image_path":"images/combination_0118.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0118_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0118_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0118_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0118_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0118_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":118,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[568,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0119","image_path":"images/combination_0119.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0119_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0119_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0119_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0119_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0119_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":119,"target_cell_count":10,"target_cells":[[0,3],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[582,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0120","image_path":"images/combination_0120.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0120_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0120_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0120_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":"combination_0120_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0120_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":120,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[555,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0121","image_path":"images/combination_0121.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0121_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0121_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0121_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0121_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0121_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":121,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[582,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0122","image_path":"images/combination_0122.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0122_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0122_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0122_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0122_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0122_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":122,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1],[5,0],[5,1],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[553,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0123","image_path":"images/combination_0123.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0123_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0123_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0123_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0123_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0123_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":123,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[567,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0124","image_path":"images/combination_0124.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0124_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0124_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0124_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":"combination_0124_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0124_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":124,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[4,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[565,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0125","image_path":"images/combination_0125.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0125_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0125_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0125_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":"combination_0125_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0125_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":125,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[586,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0126","image_path":"images/combination_0126.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0126_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0126_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0126_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0126_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0126_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":126,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[552,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0127","image_path":"images/combination_0127.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0127_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0127_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"D","question_id":"combination_0127_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0127_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":127,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[565,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0128","image_path":"images/combination_0128.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0128_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0128_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0128_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0128_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0128_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":128,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3],[3,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4],[3,4]],[[0,0]]],"total_cell_count":10}],"canvas_size":[587,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0129","image_path":"images/combination_0129.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0129_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0129_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0129_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0129_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0129_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":129,"target_cell_count":10,"target_cells":[[0,4],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0130","image_path":"images/combination_0130.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0130_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0130_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0130_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":"combination_0130_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0130_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":130,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[570,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0131","image_path":"images/combination_0131.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0131_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0131_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0131_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":"combination_0131_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0131_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":131,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[576,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0132","image_path":"images/combination_0132.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0132_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0132_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0132_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0132_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0132_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":132,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[581,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0133","image_path":"images/combination_0133.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0133_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0133_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0133_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0133_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0133_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":133,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[580,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0134","image_path":"images/combination_0134.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0134_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0134_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0134_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":"combination_0134_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0134_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":134,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[592,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0135","image_path":"images/combination_0135.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0135_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0135_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0135_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":"combination_0135_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0135_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":135,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3],[3,2],[3,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,3],[2,3],[3,0],[3,1],[3,2],[3,3]]],"total_cell_count":10}],"canvas_size":[586,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0136","image_path":"images/combination_0136.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0136_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0136_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0136_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0136_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0136_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":136,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,3],[2,3],[3,0],[3,1],[3,2],[3,3],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0137","image_path":"images/combination_0137.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0137_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0137_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0137_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0137_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0137_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":137,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0],[3,0],[4,0]]],"total_cell_count":8}],"canvas_size":[562,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0138","image_path":"images/combination_0138.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0138_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0138_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0138_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":"combination_0138_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0138_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":138,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,1],[3,1],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0139","image_path":"images/combination_0139.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0139_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0139_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0139_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0139_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0139_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":139,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[599,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0140","image_path":"images/combination_0140.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0140_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0140_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0140_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":"combination_0140_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0140_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":140,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0141","image_path":"images/combination_0141.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0141_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0141_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0141_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":"combination_0141_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0141_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":141,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9}],"canvas_size":[587,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0142","image_path":"images/combination_0142.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0142_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0142_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0142_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0142_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0142_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":142,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[561,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0143","image_path":"images/combination_0143.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0143_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0143_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0143_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":"combination_0143_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0143_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":143,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9}],"canvas_size":[578,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0144","image_path":"images/combination_0144.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0144_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0144_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0144_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":"combination_0144_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0144_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":144,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[598,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0145","image_path":"images/combination_0145.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0145_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0145_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0145_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0145_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0145_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":145,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[558,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0146","image_path":"images/combination_0146.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0146_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0146_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0146_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0146_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0146_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":146,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[1,5],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[588,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0147","image_path":"images/combination_0147.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0147_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0147_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0147_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0147_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0147_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":147,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[575,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0148","image_path":"images/combination_0148.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0148_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0148_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0148_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":"combination_0148_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0148_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":148,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0149","image_path":"images/combination_0149.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0149_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0149_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"C","question_id":"combination_0149_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0149_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":149,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[570,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0150","image_path":"images/combination_0150.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0150_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0150_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0150_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0150_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0150_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":150,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[595,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0151","image_path":"images/combination_0151.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0151_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0151_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_0151_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0151_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":151,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[598,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0152","image_path":"images/combination_0152.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0152_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0152_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0152_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":"combination_0152_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0152_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":152,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0153","image_path":"images/combination_0153.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0153_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0153_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0153_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0153_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0153_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":153,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[563,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0154","image_path":"images/combination_0154.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0154_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0154_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0154_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":"combination_0154_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0154_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":154,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10}],"canvas_size":[587,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0155","image_path":"images/combination_0155.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0155_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0155_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0155_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0155_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0155_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":155,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0156","image_path":"images/combination_0156.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0156_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0156_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0156_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0156_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0156_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":156,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0157","image_path":"images/combination_0157.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0157_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0157_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0157_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0157_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0157_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":157,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0158","image_path":"images/combination_0158.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0158_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0158_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0158_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":"combination_0158_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0158_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":158,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[575,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0159","image_path":"images/combination_0159.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0159_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0159_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0159_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0159_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0159_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":159,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,1],[5,0],[5,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0160","image_path":"images/combination_0160.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0160_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0160_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0160_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0160_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0160_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":160,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3],[3,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[583,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0161","image_path":"images/combination_0161.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0161_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0161_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0161_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":"combination_0161_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0161_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":161,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[553,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0162","image_path":"images/combination_0162.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0162_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0162_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0162_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0162_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0162_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":162,"target_cell_count":7,"target_cells":[[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0163","image_path":"images/combination_0163.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0163_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0163_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0163_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0163_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0163_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":163,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0164","image_path":"images/combination_0164.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0164_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0164_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0164_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":"combination_0164_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0164_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":164,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_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],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0165","image_path":"images/combination_0165.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0165_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0165_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0165_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":"combination_0165_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0165_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":165,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[4,2],[4,3],[5,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[561,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0166","image_path":"images/combination_0166.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0166_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0166_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0166_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0166_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0166_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":166,"target_cell_count":10,"target_cells":[[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[564,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0167","image_path":"images/combination_0167.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0167_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0167_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0167_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0167_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0167_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":167,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[597,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0168","image_path":"images/combination_0168.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0168_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0168_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0168_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0168_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0168_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":168,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10}],"canvas_size":[566,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0169","image_path":"images/combination_0169.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0169_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0169_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0169_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":"combination_0169_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0169_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":169,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[600,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0170","image_path":"images/combination_0170.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0170_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0170_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_0170_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0170_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":170,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0171","image_path":"images/combination_0171.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0171_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0171_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0171_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0171_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0171_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":171,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0172","image_path":"images/combination_0172.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0172_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0172_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0172_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0172_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0172_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":172,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[570,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0173","image_path":"images/combination_0173.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0173_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0173_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0173_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":"combination_0173_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0173_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":173,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[550,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0174","image_path":"images/combination_0174.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0174_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0174_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0174_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":"combination_0174_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0174_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":174,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[578,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0175","image_path":"images/combination_0175.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0175_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0175_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_0175_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0175_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":175,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0176","image_path":"images/combination_0176.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0176_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0176_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0176_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":"combination_0176_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0176_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":176,"target_cell_count":7,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[563,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0177","image_path":"images/combination_0177.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0177_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0177_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0177_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0177_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0177_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":177,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[557,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0178","image_path":"images/combination_0178.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0178_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0178_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0178_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0178_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0178_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":178,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[562,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0179","image_path":"images/combination_0179.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0179_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0179_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0179_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":"combination_0179_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0179_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":179,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[559,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0180","image_path":"images/combination_0180.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0180_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0180_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0180_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":"combination_0180_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0180_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":180,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0181","image_path":"images/combination_0181.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0181_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0181_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0181_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":"combination_0181_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0181_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":181,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7}],"canvas_size":[578,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0182","image_path":"images/combination_0182.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0182_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0182_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0182_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":"combination_0182_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0182_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":182,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[556,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0183","image_path":"images/combination_0183.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0183_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0183_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0183_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":"combination_0183_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0183_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":183,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0184","image_path":"images/combination_0184.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0184_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0184_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0184_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0184_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0184_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":184,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[557,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0185","image_path":"images/combination_0185.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0185_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0185_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0185_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":"combination_0185_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0185_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":185,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":9}],"canvas_size":[571,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0186","image_path":"images/combination_0186.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0186_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0186_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0186_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":"combination_0186_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0186_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":186,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[2,4]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[572,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0187","image_path":"images/combination_0187.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0187_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0187_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0187_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0187_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0187_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":187,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[600,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0188","image_path":"images/combination_0188.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0188_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0188_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0188_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0188_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0188_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":188,"target_cell_count":7,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1],[3,1]]],"total_cell_count":8}],"canvas_size":[580,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0189","image_path":"images/combination_0189.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0189_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0189_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0189_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0189_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0189_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":189,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,1],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[554,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0190","image_path":"images/combination_0190.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0190_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0190_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0190_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0190_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0190_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":190,"target_cell_count":8,"target_cells":[[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[598,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0191","image_path":"images/combination_0191.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0191_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0191_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0191_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":"combination_0191_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0191_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":191,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[573,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0192","image_path":"images/combination_0192.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0192_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0192_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0192_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":"combination_0192_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0192_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":192,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[585,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0193","image_path":"images/combination_0193.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0193_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0193_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0193_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":"combination_0193_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0193_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":193,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[4,2]]],"total_cell_count":10}],"canvas_size":[588,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0194","image_path":"images/combination_0194.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0194_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0194_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0194_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0194_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0194_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":194,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[588,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0195","image_path":"images/combination_0195.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0195_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0195_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0195_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0195_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0195_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":195,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0196","image_path":"images/combination_0196.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0196_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0196_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0196_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0196_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0196_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":196,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0197","image_path":"images/combination_0197.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0197_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0197_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0197_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":"combination_0197_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0197_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":197,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[553,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0198","image_path":"images/combination_0198.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0198_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0198_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0198_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0198_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0198_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":198,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0199","image_path":"images/combination_0199.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0199_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0199_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0199_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":"combination_0199_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0199_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":199,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0200","image_path":"images/combination_0200.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0200_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0200_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0200_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":"combination_0200_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0200_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":200,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0201","image_path":"images/combination_0201.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0201_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0201_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0201_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0201_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0201_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":201,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[598,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0202","image_path":"images/combination_0202.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0202_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0202_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0202_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":"combination_0202_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0202_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":202,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[555,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0203","image_path":"images/combination_0203.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0203_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0203_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0203_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0203_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0203_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":203,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1],[3,2],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[575,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0204","image_path":"images/combination_0204.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0204_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0204_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0204_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0204_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0204_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":204,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[577,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0205","image_path":"images/combination_0205.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0205_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0205_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0205_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":"combination_0205_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0205_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":205,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[550,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0206","image_path":"images/combination_0206.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0206_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0206_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0206_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":"combination_0206_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0206_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":206,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[582,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0207","image_path":"images/combination_0207.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0207_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0207_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0207_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0207_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0207_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":207,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0208","image_path":"images/combination_0208.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0208_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0208_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0208_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":"combination_0208_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0208_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":208,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[585,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0209","image_path":"images/combination_0209.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0209_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0209_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0209_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":"combination_0209_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0209_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":209,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0],[4,1],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0210","image_path":"images/combination_0210.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0210_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0210_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0210_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":"combination_0210_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0210_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":210,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[586,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0211","image_path":"images/combination_0211.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0211_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0211_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0211_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":"combination_0211_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0211_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":211,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[575,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0212","image_path":"images/combination_0212.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0212_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0212_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0212_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0212_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0212_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":212,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[559,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0213","image_path":"images/combination_0213.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0213_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0213_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0213_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0213_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0213_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":213,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[583,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0214","image_path":"images/combination_0214.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0214_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0214_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0214_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":"combination_0214_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0214_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":214,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[552,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0215","image_path":"images/combination_0215.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0215_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0215_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0215_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0215_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0215_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":215,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":7}],"canvas_size":[563,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0216","image_path":"images/combination_0216.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0216_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0216_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0216_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":"combination_0216_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0216_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":216,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[568,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_0217","image_path":"images/combination_0217.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0217_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0217_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0217_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0217_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0217_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":217,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[569,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0218","image_path":"images/combination_0218.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0218_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0218_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0218_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0218_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0218_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":218,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[594,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0219","image_path":"images/combination_0219.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0219_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0219_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0219_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0219_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0219_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":219,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[597,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0220","image_path":"images/combination_0220.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0220_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0220_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0220_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0220_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0220_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":220,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[565,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0221","image_path":"images/combination_0221.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0221_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0221_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0221_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0221_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0221_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":221,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[599,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0222","image_path":"images/combination_0222.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0222_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0222_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0222_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0222_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0222_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":222,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[571,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0223","image_path":"images/combination_0223.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0223_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0223_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0223_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":"combination_0223_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0223_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":223,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0224","image_path":"images/combination_0224.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0224_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0224_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0224_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0224_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0224_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":224,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[594,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0225","image_path":"images/combination_0225.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0225_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0225_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0225_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":"combination_0225_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0225_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":225,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[580,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0226","image_path":"images/combination_0226.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0226_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0226_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0226_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0226_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0226_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":226,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,3],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[575,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0227","image_path":"images/combination_0227.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0227_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0227_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0227_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0227_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0227_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":227,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[598,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0228","image_path":"images/combination_0228.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0228_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0228_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0228_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0228_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0228_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":228,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[583,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0229","image_path":"images/combination_0229.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0229_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0229_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0229_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0229_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0229_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":229,"target_cell_count":7,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[595,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0230","image_path":"images/combination_0230.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0230_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0230_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0230_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":"combination_0230_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0230_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":230,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[551,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0231","image_path":"images/combination_0231.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0231_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0231_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0231_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0231_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0231_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":231,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":7}],"canvas_size":[567,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0232","image_path":"images/combination_0232.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0232_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0232_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0232_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":"combination_0232_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0232_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":232,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0233","image_path":"images/combination_0233.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0233_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0233_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0233_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":"combination_0233_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0233_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":233,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[571,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0234","image_path":"images/combination_0234.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0234_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0234_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0234_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0234_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0234_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":234,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[572,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0235","image_path":"images/combination_0235.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0235_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0235_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0235_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0235_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0235_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":235,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[593,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0236","image_path":"images/combination_0236.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0236_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0236_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0236_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":"combination_0236_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0236_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":236,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0237","image_path":"images/combination_0237.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0237_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0237_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0237_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0237_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0237_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":237,"target_cell_count":7,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[600,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0238","image_path":"images/combination_0238.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0238_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0238_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0238_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0238_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0238_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":238,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[557,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0239","image_path":"images/combination_0239.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0239_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0239_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0239_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":"combination_0239_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0239_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":239,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6}],"canvas_size":[589,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0240","image_path":"images/combination_0240.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0240_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0240_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0240_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":"combination_0240_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0240_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":240,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[594,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0241","image_path":"images/combination_0241.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0241_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0241_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0241_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":"combination_0241_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0241_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":241,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[571,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0242","image_path":"images/combination_0242.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0242_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0242_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0242_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0242_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0242_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":242,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9}],"canvas_size":[583,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0243","image_path":"images/combination_0243.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0243_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0243_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0243_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0243_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0243_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":243,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[598,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0244","image_path":"images/combination_0244.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0244_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0244_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0244_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0244_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0244_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":244,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":8}],"canvas_size":[558,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0245","image_path":"images/combination_0245.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0245_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0245_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0245_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":"combination_0245_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0245_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":245,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[553,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0246","image_path":"images/combination_0246.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0246_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0246_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0246_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0246_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0246_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":246,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0247","image_path":"images/combination_0247.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0247_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0247_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0247_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":"combination_0247_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0247_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":247,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[576,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0248","image_path":"images/combination_0248.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0248_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0248_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0248_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":"combination_0248_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0248_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":248,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[567,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0249","image_path":"images/combination_0249.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0249_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0249_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0249_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":"combination_0249_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0249_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":249,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0250","image_path":"images/combination_0250.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0250_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0250_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0250_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":"combination_0250_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0250_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":250,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[578,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0251","image_path":"images/combination_0251.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0251_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0251_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0251_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":"combination_0251_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0251_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":251,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[599,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0252","image_path":"images/combination_0252.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0252_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0252_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0252_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":"combination_0252_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0252_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":252,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[584,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0253","image_path":"images/combination_0253.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0253_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0253_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0253_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0253_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0253_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":253,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[573,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0254","image_path":"images/combination_0254.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0254_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0254_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0254_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":"combination_0254_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0254_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":254,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,5]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0255","image_path":"images/combination_0255.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0255_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0255_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0255_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":"combination_0255_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0255_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":255,"target_cell_count":10,"target_cells":[[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[581,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0256","image_path":"images/combination_0256.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0256_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0256_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0256_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":"combination_0256_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0256_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":256,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[570,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0257","image_path":"images/combination_0257.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0257_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0257_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0257_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0257_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0257_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":257,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[591,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0258","image_path":"images/combination_0258.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0258_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0258_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0258_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0258_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0258_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":258,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[552,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0259","image_path":"images/combination_0259.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0259_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0259_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0259_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0259_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0259_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":259,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[563,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0260","image_path":"images/combination_0260.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0260_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0260_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0260_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":"combination_0260_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0260_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":260,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[577,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_0261","image_path":"images/combination_0261.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0261_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0261_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0261_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0261_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0261_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":261,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10}],"canvas_size":[570,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0262","image_path":"images/combination_0262.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0262_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0262_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0262_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0262_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0262_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":262,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[597,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0263","image_path":"images/combination_0263.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0263_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0263_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0263_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0263_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0263_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":263,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[589,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0264","image_path":"images/combination_0264.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0264_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0264_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0264_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":"combination_0264_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0264_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":264,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0265","image_path":"images/combination_0265.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0265_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0265_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0265_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0265_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0265_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":265,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0266","image_path":"images/combination_0266.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0266_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0266_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0266_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":"combination_0266_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0266_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":266,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0267","image_path":"images/combination_0267.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0267_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0267_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0267_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":"combination_0267_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0267_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":267,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[598,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0268","image_path":"images/combination_0268.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0268_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0268_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0268_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0268_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0268_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":268,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0269","image_path":"images/combination_0269.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0269_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0269_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0269_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":"combination_0269_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0269_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":269,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[561,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0270","image_path":"images/combination_0270.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0270_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0270_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0270_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0270_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0270_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":270,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[580,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0271","image_path":"images/combination_0271.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0271_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0271_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0271_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":"combination_0271_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0271_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":271,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[1,4],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0272","image_path":"images/combination_0272.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0272_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0272_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0272_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":"combination_0272_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0272_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":272,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0273","image_path":"images/combination_0273.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0273_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0273_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0273_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":"combination_0273_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0273_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":273,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0274","image_path":"images/combination_0274.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0274_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0274_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0274_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0274_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0274_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":274,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2],[3,1],[4,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10}],"canvas_size":[598,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0275","image_path":"images/combination_0275.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0275_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0275_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0275_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":"combination_0275_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0275_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":275,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7}],"canvas_size":[573,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0276","image_path":"images/combination_0276.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0276_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0276_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0276_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0276_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0276_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":276,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0277","image_path":"images/combination_0277.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0277_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0277_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0277_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0277_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0277_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":277,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[568,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0278","image_path":"images/combination_0278.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0278_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0278_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0278_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":"combination_0278_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0278_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":278,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[576,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0279","image_path":"images/combination_0279.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0279_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0279_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0279_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0279_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0279_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":279,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0280","image_path":"images/combination_0280.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0280_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0280_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0280_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":"combination_0280_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0280_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":280,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0281","image_path":"images/combination_0281.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0281_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0281_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0281_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0281_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0281_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":281,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0282","image_path":"images/combination_0282.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0282_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0282_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0282_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0282_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0282_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":282,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[596,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0283","image_path":"images/combination_0283.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0283_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0283_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0283_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":"combination_0283_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0283_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":283,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0284","image_path":"images/combination_0284.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0284_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0284_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0284_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0284_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0284_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":284,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[587,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0285","image_path":"images/combination_0285.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0285_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0285_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0285_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":"combination_0285_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0285_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":285,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[581,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0286","image_path":"images/combination_0286.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0286_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0286_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0286_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":"combination_0286_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0286_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":286,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[585,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0287","image_path":"images/combination_0287.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0287_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0287_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0287_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":"combination_0287_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0287_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":287,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0288","image_path":"images/combination_0288.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0288_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0288_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0288_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0288_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0288_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":288,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[598,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0289","image_path":"images/combination_0289.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0289_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0289_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0289_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0289_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0289_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":289,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[584,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0290","image_path":"images/combination_0290.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0290_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0290_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0290_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":"combination_0290_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0290_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":290,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[592,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0291","image_path":"images/combination_0291.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0291_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0291_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0291_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0291_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0291_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":291,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[599,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0292","image_path":"images/combination_0292.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0292_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0292_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0292_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0292_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0292_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":292,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":6}],"canvas_size":[580,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0293","image_path":"images/combination_0293.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0293_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0293_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0293_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":"combination_0293_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0293_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":293,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[561,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0294","image_path":"images/combination_0294.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0294_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0294_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0294_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":"combination_0294_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0294_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":294,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[568,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0295","image_path":"images/combination_0295.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0295_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0295_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_0295_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0295_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":295,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[554,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0296","image_path":"images/combination_0296.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0296_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0296_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0296_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0296_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0296_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":296,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0297","image_path":"images/combination_0297.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0297_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0297_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0297_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0297_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0297_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":297,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[563,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0298","image_path":"images/combination_0298.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0298_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0298_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0298_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":"combination_0298_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0298_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":298,"target_cell_count":10,"target_cells":[[0,0],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[573,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0299","image_path":"images/combination_0299.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0299_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0299_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0299_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":"combination_0299_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0299_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":299,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[588,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0300","image_path":"images/combination_0300.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0300_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0300_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0300_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0300_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0300_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":300,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8}],"canvas_size":[575,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0301","image_path":"images/combination_0301.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0301_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0301_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0301_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":"combination_0301_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0301_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":301,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[585,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0302","image_path":"images/combination_0302.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0302_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0302_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0302_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":"combination_0302_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0302_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":302,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0303","image_path":"images/combination_0303.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0303_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0303_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0303_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0303_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0303_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":303,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[558,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0304","image_path":"images/combination_0304.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0304_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0304_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0304_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0304_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0304_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":304,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,1],[2,3],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[561,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0305","image_path":"images/combination_0305.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0305_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0305_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0305_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":"combination_0305_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0305_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":305,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[577,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0306","image_path":"images/combination_0306.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0306_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0306_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0306_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":"combination_0306_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0306_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":306,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[590,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0307","image_path":"images/combination_0307.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0307_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0307_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0307_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0307_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0307_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":307,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[561,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0308","image_path":"images/combination_0308.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0308_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0308_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0308_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":"combination_0308_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0308_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":308,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[554,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0309","image_path":"images/combination_0309.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0309_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0309_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0309_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0309_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0309_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":309,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[585,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0310","image_path":"images/combination_0310.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0310_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0310_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0310_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":"combination_0310_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0310_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":310,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[566,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0311","image_path":"images/combination_0311.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0311_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0311_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0311_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0311_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0311_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":311,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0],[5,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[5,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0312","image_path":"images/combination_0312.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0312_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0312_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0312_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":"combination_0312_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0312_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":312,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[586,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0313","image_path":"images/combination_0313.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0313_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0313_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0313_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0313_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0313_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":313,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[562,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0314","image_path":"images/combination_0314.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0314_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0314_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0314_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":"combination_0314_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0314_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":314,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0315","image_path":"images/combination_0315.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0315_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0315_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0315_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":"combination_0315_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0315_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":315,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0316","image_path":"images/combination_0316.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0316_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0316_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0316_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":"combination_0316_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0316_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":316,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[579,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0317","image_path":"images/combination_0317.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0317_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0317_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0317_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":"combination_0317_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0317_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":317,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[594,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0318","image_path":"images/combination_0318.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0318_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0318_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0318_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0318_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0318_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":318,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[561,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0319","image_path":"images/combination_0319.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0319_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0319_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0319_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":"combination_0319_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0319_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":319,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0320","image_path":"images/combination_0320.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0320_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0320_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0320_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":"combination_0320_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0320_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":320,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0321","image_path":"images/combination_0321.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0321_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0321_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0321_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":"combination_0321_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0321_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":321,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[595,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0322","image_path":"images/combination_0322.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0322_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0322_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0322_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":"combination_0322_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0322_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":322,"target_cell_count":9,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0323","image_path":"images/combination_0323.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0323_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0323_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0323_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":"combination_0323_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0323_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":323,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[587,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0324","image_path":"images/combination_0324.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0324_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0324_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0324_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":"combination_0324_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0324_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":324,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0325","image_path":"images/combination_0325.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0325_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0325_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_0325_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":"combination_0325_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0325_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":325,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,1],[2,2],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0326","image_path":"images/combination_0326.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0326_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0326_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0326_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":"combination_0326_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0326_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":326,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[553,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0327","image_path":"images/combination_0327.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0327_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0327_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0327_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":"combination_0327_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0327_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":327,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[591,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0328","image_path":"images/combination_0328.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0328_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0328_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0328_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":"combination_0328_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0328_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":328,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[580,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0329","image_path":"images/combination_0329.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0329_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0329_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0329_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0329_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0329_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":329,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[589,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0330","image_path":"images/combination_0330.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0330_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0330_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0330_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":"combination_0330_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0330_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":330,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7}],"canvas_size":[596,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0331","image_path":"images/combination_0331.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0331_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0331_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0331_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0331_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0331_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":331,"target_cell_count":7,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[565,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0332","image_path":"images/combination_0332.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0332_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0332_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0332_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0332_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0332_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":332,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[585,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0333","image_path":"images/combination_0333.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0333_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0333_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0333_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0333_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0333_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":333,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[565,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0334","image_path":"images/combination_0334.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0334_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0334_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0334_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0334_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0334_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":334,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[559,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0335","image_path":"images/combination_0335.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0335_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0335_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0335_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0335_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0335_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":335,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,2],[3,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0336","image_path":"images/combination_0336.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0336_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0336_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0336_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0336_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0336_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":336,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,4],[2,1],[2,2],[2,3],[2,4],[2,5],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10}],"canvas_size":[562,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0337","image_path":"images/combination_0337.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0337_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0337_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0337_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0337_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0337_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":337,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0338","image_path":"images/combination_0338.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0338_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0338_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0338_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0338_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0338_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":338,"target_cell_count":8,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[559,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0339","image_path":"images/combination_0339.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0339_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0339_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0339_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0339_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0339_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":339,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[575,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0340","image_path":"images/combination_0340.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0340_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0340_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0340_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":"combination_0340_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0340_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":340,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0341","image_path":"images/combination_0341.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0341_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0341_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0341_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0341_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0341_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":341,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[557,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0342","image_path":"images/combination_0342.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0342_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0342_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0342_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":"combination_0342_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0342_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":342,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0343","image_path":"images/combination_0343.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0343_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0343_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0343_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":"combination_0343_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0343_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":343,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0344","image_path":"images/combination_0344.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0344_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0344_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0344_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0344_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0344_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":344,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[599,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0345","image_path":"images/combination_0345.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0345_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0345_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0345_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0345_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0345_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":345,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0346","image_path":"images/combination_0346.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0346_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0346_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0346_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0346_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0346_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":346,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4],[2,5],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":9}],"canvas_size":[572,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0347","image_path":"images/combination_0347.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0347_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0347_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0347_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":"combination_0347_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0347_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":347,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[570,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0348","image_path":"images/combination_0348.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0348_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0348_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0348_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0348_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0348_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":348,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[576,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0349","image_path":"images/combination_0349.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0349_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0349_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0349_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0349_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0349_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":349,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[573,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0350","image_path":"images/combination_0350.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0350_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0350_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0350_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0350_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0350_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":350,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":8}],"canvas_size":[589,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0351","image_path":"images/combination_0351.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0351_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0351_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0351_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":"combination_0351_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0351_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":351,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0352","image_path":"images/combination_0352.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0352_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0352_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0352_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":"combination_0352_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0352_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":352,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_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],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[556,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0353","image_path":"images/combination_0353.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0353_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0353_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0353_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0353_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0353_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":353,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[563,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0354","image_path":"images/combination_0354.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0354_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0354_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0354_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":"combination_0354_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0354_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":354,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[560,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0355","image_path":"images/combination_0355.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0355_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0355_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0355_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":"combination_0355_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0355_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":355,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":9}],"canvas_size":[591,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0356","image_path":"images/combination_0356.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0356_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0356_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0356_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0356_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0356_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":356,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[561,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0357","image_path":"images/combination_0357.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0357_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0357_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0357_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":"combination_0357_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0357_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":357,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[598,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0358","image_path":"images/combination_0358.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0358_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0358_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0358_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0358_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0358_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":358,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[555,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0359","image_path":"images/combination_0359.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0359_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0359_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0359_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":"combination_0359_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0359_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":359,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":7}],"canvas_size":[564,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0360","image_path":"images/combination_0360.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0360_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0360_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0360_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":"combination_0360_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0360_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":360,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[589,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0361","image_path":"images/combination_0361.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0361_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0361_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0361_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":"combination_0361_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0361_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":361,"target_cell_count":9,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[599,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0362","image_path":"images/combination_0362.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0362_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0362_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0362_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0362_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0362_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":362,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[599,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0363","image_path":"images/combination_0363.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0363_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0363_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0363_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0363_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0363_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":363,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0364","image_path":"images/combination_0364.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0364_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0364_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0364_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0364_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0364_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":364,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0365","image_path":"images/combination_0365.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0365_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0365_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0365_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":"combination_0365_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0365_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":365,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0366","image_path":"images/combination_0366.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0366_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0366_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0366_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":"combination_0366_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0366_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":366,"target_cell_count":6,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0367","image_path":"images/combination_0367.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0367_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0367_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0367_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0367_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0367_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":367,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[580,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0368","image_path":"images/combination_0368.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0368_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0368_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0368_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":"combination_0368_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0368_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":368,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[599,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0369","image_path":"images/combination_0369.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0369_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0369_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0369_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":"combination_0369_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0369_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":369,"target_cell_count":8,"target_cells":[[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[557,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0370","image_path":"images/combination_0370.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0370_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0370_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0370_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":"combination_0370_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0370_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":370,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[569,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0371","image_path":"images/combination_0371.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0371_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0371_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0371_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0371_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0371_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":371,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0372","image_path":"images/combination_0372.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0372_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0372_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0372_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0372_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0372_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":372,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":5}],"canvas_size":[552,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0373","image_path":"images/combination_0373.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0373_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0373_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0373_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0373_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0373_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":373,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[571,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0374","image_path":"images/combination_0374.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0374_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0374_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0374_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":"combination_0374_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0374_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":374,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[564,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0375","image_path":"images/combination_0375.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0375_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0375_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0375_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":"combination_0375_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0375_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":375,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[593,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0376","image_path":"images/combination_0376.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0376_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0376_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0376_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":"combination_0376_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0376_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":376,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0377","image_path":"images/combination_0377.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0377_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0377_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0377_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":"combination_0377_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0377_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":377,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[551,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0378","image_path":"images/combination_0378.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0378_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0378_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0378_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0378_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0378_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":378,"target_cell_count":9,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[1,4],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[551,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0379","image_path":"images/combination_0379.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0379_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0379_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0379_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":"combination_0379_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0379_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":379,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[2,4]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[558,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0380","image_path":"images/combination_0380.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0380_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0380_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0380_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0380_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0380_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":380,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[1,4],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[580,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0381","image_path":"images/combination_0381.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0381_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0381_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0381_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0381_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0381_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":381,"target_cell_count":10,"target_cells":[[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0382","image_path":"images/combination_0382.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0382_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0382_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0382_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0382_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0382_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":382,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0383","image_path":"images/combination_0383.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0383_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0383_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0383_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":"combination_0383_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0383_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":383,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0384","image_path":"images/combination_0384.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0384_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0384_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0384_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":"combination_0384_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0384_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":384,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0385","image_path":"images/combination_0385.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0385_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0385_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0385_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0385_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0385_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":385,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[589,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0386","image_path":"images/combination_0386.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0386_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0386_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0386_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":"combination_0386_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0386_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":386,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[578,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0387","image_path":"images/combination_0387.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0387_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0387_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0387_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":"combination_0387_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0387_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":387,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[573,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0388","image_path":"images/combination_0388.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0388_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0388_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0388_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0388_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0388_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":388,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0389","image_path":"images/combination_0389.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0389_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0389_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0389_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0389_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0389_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":389,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":6}],"canvas_size":[586,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0390","image_path":"images/combination_0390.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0390_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0390_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0390_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0390_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0390_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":390,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0391","image_path":"images/combination_0391.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0391_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0391_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0391_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":"combination_0391_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0391_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":391,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9}],"canvas_size":[589,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0392","image_path":"images/combination_0392.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0392_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0392_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0392_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0392_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0392_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":392,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[573,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0393","image_path":"images/combination_0393.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0393_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0393_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0393_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0393_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0393_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":393,"target_cell_count":7,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[565,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0394","image_path":"images/combination_0394.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0394_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0394_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0394_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0394_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0394_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":394,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0395","image_path":"images/combination_0395.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0395_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0395_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0395_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0395_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0395_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":395,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0396","image_path":"images/combination_0396.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0396_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0396_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0396_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0396_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0396_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":396,"target_cell_count":8,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_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],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[557,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0397","image_path":"images/combination_0397.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0397_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0397_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0397_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0397_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0397_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":397,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[575,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0398","image_path":"images/combination_0398.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0398_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0398_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0398_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0398_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0398_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":398,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[552,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0399","image_path":"images/combination_0399.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0399_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0399_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0399_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0399_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0399_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":399,"target_cell_count":10,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,4],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[569,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0400","image_path":"images/combination_0400.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0400_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0400_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0400_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0400_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0400_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":400,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[581,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0401","image_path":"images/combination_0401.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0401_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0401_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0401_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0401_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0401_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":401,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[581,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0402","image_path":"images/combination_0402.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0402_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0402_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_0402_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0402_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":402,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[565,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0403","image_path":"images/combination_0403.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0403_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0403_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0403_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0403_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0403_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":403,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0404","image_path":"images/combination_0404.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0404_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0404_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0404_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0404_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0404_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":404,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,2],[3,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[552,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0405","image_path":"images/combination_0405.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0405_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0405_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0405_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0405_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0405_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":405,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[576,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0406","image_path":"images/combination_0406.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0406_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0406_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0406_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":"combination_0406_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0406_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":406,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0407","image_path":"images/combination_0407.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0407_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0407_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_0407_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0407_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":407,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0408","image_path":"images/combination_0408.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0408_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0408_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0408_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":"combination_0408_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0408_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":408,"target_cell_count":8,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0409","image_path":"images/combination_0409.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0409_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0409_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0409_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":"combination_0409_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0409_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":409,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[559,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0410","image_path":"images/combination_0410.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0410_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0410_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0410_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":"combination_0410_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0410_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":410,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[563,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0411","image_path":"images/combination_0411.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0411_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0411_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0411_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0411_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0411_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":411,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0412","image_path":"images/combination_0412.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0412_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0412_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0412_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":"combination_0412_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0412_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":412,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[598,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0413","image_path":"images/combination_0413.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0413_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0413_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0413_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":"combination_0413_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0413_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":413,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[577,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0414","image_path":"images/combination_0414.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0414_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0414_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0414_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0414_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0414_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":414,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[599,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0415","image_path":"images/combination_0415.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0415_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0415_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0415_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":"combination_0415_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0415_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":415,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[566,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0416","image_path":"images/combination_0416.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0416_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0416_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0416_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":"combination_0416_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0416_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":416,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[588,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0417","image_path":"images/combination_0417.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0417_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0417_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0417_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0417_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0417_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":417,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[570,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0418","image_path":"images/combination_0418.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0418_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0418_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0418_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0418_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0418_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":418,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0419","image_path":"images/combination_0419.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0419_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0419_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0419_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":"combination_0419_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0419_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":419,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0420","image_path":"images/combination_0420.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0420_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0420_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0420_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":"combination_0420_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0420_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":420,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[591,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0421","image_path":"images/combination_0421.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0421_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0421_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0421_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":"combination_0421_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0421_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":421,"target_cell_count":10,"target_cells":[[0,3],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0422","image_path":"images/combination_0422.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0422_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0422_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0422_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":"combination_0422_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0422_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":422,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,1],[5,0],[5,1],[6,1],[7,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[5,1],[6,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0423","image_path":"images/combination_0423.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0423_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0423_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0423_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0423_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0423_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":423,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,1],[4,1],[5,0],[5,1],[6,1],[7,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0424","image_path":"images/combination_0424.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0424_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0424_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0424_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":"combination_0424_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0424_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":424,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[576,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0425","image_path":"images/combination_0425.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0425_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0425_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0425_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0425_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0425_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":425,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[560,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0426","image_path":"images/combination_0426.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0426_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0426_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0426_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0426_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0426_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":426,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0427","image_path":"images/combination_0427.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0427_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0427_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0427_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0427_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0427_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":427,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[566,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0428","image_path":"images/combination_0428.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0428_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0428_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0428_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0428_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0428_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":428,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":6}],"canvas_size":[588,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0429","image_path":"images/combination_0429.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0429_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0429_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0429_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0429_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0429_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":429,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[567,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0430","image_path":"images/combination_0430.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0430_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0430_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0430_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":"combination_0430_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0430_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":430,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[568,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0431","image_path":"images/combination_0431.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0431_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0431_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0431_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":"combination_0431_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0431_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":431,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[587,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0432","image_path":"images/combination_0432.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0432_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0432_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0432_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":"combination_0432_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0432_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":432,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0433","image_path":"images/combination_0433.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0433_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0433_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0433_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":"combination_0433_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0433_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":433,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[573,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0434","image_path":"images/combination_0434.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0434_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0434_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0434_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0434_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0434_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":434,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0435","image_path":"images/combination_0435.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0435_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0435_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0435_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":"combination_0435_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0435_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":435,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[4,0],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0436","image_path":"images/combination_0436.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0436_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0436_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0436_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":"combination_0436_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0436_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":436,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[583,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0437","image_path":"images/combination_0437.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0437_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0437_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0437_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0437_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0437_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":437,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[563,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0438","image_path":"images/combination_0438.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0438_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0438_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0438_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0438_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0438_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":438,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0439","image_path":"images/combination_0439.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0439_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0439_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0439_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":"combination_0439_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0439_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":439,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[557,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0440","image_path":"images/combination_0440.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0440_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0440_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0440_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0440_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0440_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":440,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]],"total_cell_count":10}],"canvas_size":[561,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0441","image_path":"images/combination_0441.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0441_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0441_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0441_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0441_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0441_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":441,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[573,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0442","image_path":"images/combination_0442.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0442_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0442_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0442_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0442_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0442_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":442,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[2,3],[3,0],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0443","image_path":"images/combination_0443.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0443_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0443_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0443_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0443_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0443_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":443,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0444","image_path":"images/combination_0444.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0444_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0444_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0444_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0444_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0444_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":444,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[585,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0445","image_path":"images/combination_0445.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0445_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0445_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0445_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":"combination_0445_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0445_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":445,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_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],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[600,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0446","image_path":"images/combination_0446.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0446_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0446_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0446_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":"combination_0446_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0446_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":446,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1]]],"total_cell_count":10}],"canvas_size":[576,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0447","image_path":"images/combination_0447.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0447_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0447_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0447_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":"combination_0447_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0447_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":447,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6}],"canvas_size":[567,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0448","image_path":"images/combination_0448.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0448_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0448_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0448_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0448_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0448_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":448,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0449","image_path":"images/combination_0449.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0449_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0449_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0449_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":"combination_0449_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0449_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":449,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[556,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0450","image_path":"images/combination_0450.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0450_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0450_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0450_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":"combination_0450_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0450_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":450,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0451","image_path":"images/combination_0451.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0451_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0451_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0451_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":"combination_0451_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0451_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":451,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[571,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0452","image_path":"images/combination_0452.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0452_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0452_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0452_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0452_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0452_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":452,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":10}],"canvas_size":[565,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0453","image_path":"images/combination_0453.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0453_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0453_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0453_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":"combination_0453_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0453_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":453,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[569,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0454","image_path":"images/combination_0454.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0454_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0454_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0454_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0454_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0454_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":454,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[596,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0455","image_path":"images/combination_0455.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0455_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0455_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0455_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0455_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0455_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":455,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[597,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0456","image_path":"images/combination_0456.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0456_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0456_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_0456_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":"combination_0456_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0456_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":456,"target_cell_count":9,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[598,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0457","image_path":"images/combination_0457.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0457_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0457_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0457_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":"combination_0457_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0457_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":457,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[554,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0458","image_path":"images/combination_0458.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0458_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0458_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0458_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0458_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0458_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":458,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[591,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0459","image_path":"images/combination_0459.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0459_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0459_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0459_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0459_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0459_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":459,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0460","image_path":"images/combination_0460.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0460_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0460_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0460_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0460_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0460_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":460,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0461","image_path":"images/combination_0461.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0461_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0461_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0461_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0461_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0461_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":461,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[587,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0462","image_path":"images/combination_0462.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0462_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0462_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0462_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":"combination_0462_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0462_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":462,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[3,0],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0463","image_path":"images/combination_0463.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0463_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0463_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0463_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":"combination_0463_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0463_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":463,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[567,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0464","image_path":"images/combination_0464.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0464_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0464_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0464_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":"combination_0464_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0464_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":464,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[562,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0465","image_path":"images/combination_0465.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0465_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0465_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0465_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":"combination_0465_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0465_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":465,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[553,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0466","image_path":"images/combination_0466.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0466_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0466_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0466_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":"combination_0466_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0466_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":466,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[566,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0467","image_path":"images/combination_0467.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0467_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0467_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0467_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":"combination_0467_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0467_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":467,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[563,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0468","image_path":"images/combination_0468.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0468_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0468_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0468_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0468_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0468_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":468,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[566,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0469","image_path":"images/combination_0469.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0469_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0469_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0469_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":"combination_0469_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0469_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":469,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[552,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0470","image_path":"images/combination_0470.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0470_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0470_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0470_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0470_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0470_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":470,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0471","image_path":"images/combination_0471.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0471_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0471_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0471_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0471_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0471_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":471,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[559,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0472","image_path":"images/combination_0472.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0472_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0472_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0472_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0472_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0472_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":472,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[571,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0473","image_path":"images/combination_0473.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0473_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0473_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0473_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":"combination_0473_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0473_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":473,"target_cell_count":6,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0474","image_path":"images/combination_0474.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0474_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0474_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0474_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":"combination_0474_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0474_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":474,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[554,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0475","image_path":"images/combination_0475.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0475_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0475_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0475_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0475_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0475_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":475,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[581,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0476","image_path":"images/combination_0476.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0476_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0476_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0476_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0476_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0476_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":476,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[589,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0477","image_path":"images/combination_0477.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0477_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0477_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0477_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0477_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0477_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":477,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[570,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0478","image_path":"images/combination_0478.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0478_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0478_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0478_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0478_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0478_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":478,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[600,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0479","image_path":"images/combination_0479.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0479_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0479_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0479_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0479_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0479_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":479,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[575,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0480","image_path":"images/combination_0480.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0480_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0480_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0480_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0480_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0480_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":480,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[593,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0481","image_path":"images/combination_0481.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0481_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0481_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0481_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":"combination_0481_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0481_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":481,"target_cell_count":9,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[583,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0482","image_path":"images/combination_0482.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0482_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0482_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0482_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0482_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0482_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":482,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,3],[1,4],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[583,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0483","image_path":"images/combination_0483.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0483_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0483_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0483_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":"combination_0483_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0483_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":483,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[586,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0484","image_path":"images/combination_0484.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0484_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0484_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0484_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":"combination_0484_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0484_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":484,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[558,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0485","image_path":"images/combination_0485.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0485_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0485_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0485_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":"combination_0485_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0485_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":485,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[561,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0486","image_path":"images/combination_0486.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0486_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0486_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0486_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":"combination_0486_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0486_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":486,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[588,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0487","image_path":"images/combination_0487.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0487_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0487_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0487_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0487_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0487_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":487,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0488","image_path":"images/combination_0488.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0488_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0488_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0488_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0488_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0488_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":488,"target_cell_count":8,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[561,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0489","image_path":"images/combination_0489.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0489_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0489_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0489_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0489_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0489_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":489,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0490","image_path":"images/combination_0490.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0490_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0490_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_0490_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":"combination_0490_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0490_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":490,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[581,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0491","image_path":"images/combination_0491.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0491_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0491_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0491_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0491_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0491_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":491,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0492","image_path":"images/combination_0492.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0492_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0492_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0492_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0492_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0492_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":492,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[566,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0493","image_path":"images/combination_0493.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0493_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0493_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_0493_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0493_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":493,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[590,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0494","image_path":"images/combination_0494.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0494_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0494_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0494_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":"combination_0494_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0494_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":494,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[593,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0495","image_path":"images/combination_0495.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0495_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0495_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0495_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0495_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0495_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":495,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[596,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0496","image_path":"images/combination_0496.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0496_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0496_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0496_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0496_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0496_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":496,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[566,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0497","image_path":"images/combination_0497.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0497_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0497_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0497_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0497_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0497_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":497,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0],[4,0],[4,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[580,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0498","image_path":"images/combination_0498.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0498_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0498_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_0498_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0498_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":498,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0499","image_path":"images/combination_0499.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0499_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0499_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0499_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":"combination_0499_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0499_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":499,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[579,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0500","image_path":"images/combination_0500.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0500_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0500_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0500_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":"combination_0500_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0500_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":500,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[590,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0501","image_path":"images/combination_0501.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0501_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0501_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0501_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":"combination_0501_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0501_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":501,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[582,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0502","image_path":"images/combination_0502.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0502_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0502_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0502_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":"combination_0502_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0502_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":502,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[560,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0503","image_path":"images/combination_0503.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0503_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0503_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0503_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":"combination_0503_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0503_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":503,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[579,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0504","image_path":"images/combination_0504.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0504_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0504_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0504_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":"combination_0504_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0504_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":504,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[559,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0505","image_path":"images/combination_0505.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0505_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0505_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0505_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":"combination_0505_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0505_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":505,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[598,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0506","image_path":"images/combination_0506.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0506_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0506_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0506_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":"combination_0506_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0506_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":506,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[580,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0507","image_path":"images/combination_0507.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0507_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0507_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0507_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0507_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0507_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":507,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0508","image_path":"images/combination_0508.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0508_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0508_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0508_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0508_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0508_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":508,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[595,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0509","image_path":"images/combination_0509.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0509_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0509_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0509_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0509_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0509_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":509,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[593,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0510","image_path":"images/combination_0510.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0510_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0510_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_0510_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":"combination_0510_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0510_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":510,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[556,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0511","image_path":"images/combination_0511.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0511_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0511_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0511_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":"combination_0511_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0511_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":511,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[551,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0512","image_path":"images/combination_0512.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0512_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0512_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0512_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0512_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0512_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":512,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[551,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0513","image_path":"images/combination_0513.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0513_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0513_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0513_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0513_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0513_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":513,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[572,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0514","image_path":"images/combination_0514.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0514_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0514_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0514_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0514_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0514_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":514,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[560,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0515","image_path":"images/combination_0515.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0515_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0515_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0515_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":"combination_0515_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0515_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":515,"target_cell_count":8,"target_cells":[[0,3],[1,2],[1,3],[2,2],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0516","image_path":"images/combination_0516.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0516_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0516_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0516_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":"combination_0516_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0516_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":516,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,0],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[4,0],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[577,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0517","image_path":"images/combination_0517.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0517_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0517_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0517_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0517_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0517_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":517,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":8}],"canvas_size":[573,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0518","image_path":"images/combination_0518.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0518_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0518_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0518_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0518_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0518_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":518,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6}],"canvas_size":[588,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0519","image_path":"images/combination_0519.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0519_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0519_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0519_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":"combination_0519_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0519_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":519,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[550,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0520","image_path":"images/combination_0520.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0520_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0520_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0520_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":"combination_0520_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0520_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":520,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0521","image_path":"images/combination_0521.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0521_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0521_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0521_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":"combination_0521_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0521_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":521,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[554,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0522","image_path":"images/combination_0522.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0522_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0522_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0522_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0522_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0522_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":522,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[593,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0523","image_path":"images/combination_0523.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0523_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0523_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0523_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0523_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0523_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":523,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[564,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0524","image_path":"images/combination_0524.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0524_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0524_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0524_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":"combination_0524_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0524_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":524,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[584,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0525","image_path":"images/combination_0525.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0525_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0525_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0525_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0525_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0525_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":525,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[559,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0526","image_path":"images/combination_0526.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0526_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0526_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0526_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":"combination_0526_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0526_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":526,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[577,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0527","image_path":"images/combination_0527.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0527_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0527_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0527_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0527_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0527_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":527,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[600,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0528","image_path":"images/combination_0528.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0528_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0528_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0528_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0528_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0528_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":528,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2],[4,0],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":7}],"canvas_size":[591,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0529","image_path":"images/combination_0529.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0529_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0529_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0529_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0529_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0529_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":529,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[4,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":9}],"canvas_size":[571,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0530","image_path":"images/combination_0530.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0530_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0530_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0530_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0530_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0530_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":530,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0531","image_path":"images/combination_0531.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0531_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0531_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0531_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":"combination_0531_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0531_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":531,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[563,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0532","image_path":"images/combination_0532.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0532_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0532_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0532_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0532_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0532_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":532,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0533","image_path":"images/combination_0533.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0533_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0533_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0533_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":"combination_0533_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0533_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":533,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[577,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0534","image_path":"images/combination_0534.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0534_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0534_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0534_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":"combination_0534_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0534_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":534,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[559,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0535","image_path":"images/combination_0535.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0535_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0535_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0535_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0535_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0535_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":535,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[597,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0536","image_path":"images/combination_0536.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0536_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0536_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_0536_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":"combination_0536_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0536_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":536,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0537","image_path":"images/combination_0537.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0537_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0537_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0537_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":"combination_0537_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0537_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":537,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[567,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0538","image_path":"images/combination_0538.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0538_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0538_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0538_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":"combination_0538_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0538_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":538,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[568,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0539","image_path":"images/combination_0539.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0539_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0539_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0539_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0539_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0539_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":539,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[589,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0540","image_path":"images/combination_0540.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0540_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0540_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0540_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":"combination_0540_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0540_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":540,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0541","image_path":"images/combination_0541.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0541_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0541_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0541_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0541_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0541_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":541,"target_cell_count":9,"target_cells":[[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[580,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0542","image_path":"images/combination_0542.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0542_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0542_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0542_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":"combination_0542_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0542_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":542,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0543","image_path":"images/combination_0543.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0543_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0543_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0543_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0543_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0543_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":543,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[592,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0544","image_path":"images/combination_0544.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0544_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0544_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0544_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":"combination_0544_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0544_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":544,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[563,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0545","image_path":"images/combination_0545.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0545_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0545_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0545_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":"combination_0545_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0545_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":545,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[550,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0546","image_path":"images/combination_0546.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0546_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0546_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0546_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0546_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0546_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":546,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[552,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0547","image_path":"images/combination_0547.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0547_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0547_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0547_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":"combination_0547_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0547_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":547,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[552,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0548","image_path":"images/combination_0548.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0548_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0548_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0548_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":"combination_0548_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0548_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":548,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0549","image_path":"images/combination_0549.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0549_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0549_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0549_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":"combination_0549_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0549_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":549,"target_cell_count":9,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,4],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[580,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0550","image_path":"images/combination_0550.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0550_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0550_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0550_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0550_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0550_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":550,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[582,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0551","image_path":"images/combination_0551.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0551_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0551_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0551_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":"combination_0551_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0551_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":551,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[551,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0552","image_path":"images/combination_0552.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0552_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0552_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0552_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":"combination_0552_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0552_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":552,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_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],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9}],"canvas_size":[580,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0553","image_path":"images/combination_0553.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0553_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0553_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0553_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0553_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0553_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":553,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[582,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0554","image_path":"images/combination_0554.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0554_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0554_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0554_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":"combination_0554_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0554_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":554,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2]]],"total_cell_count":7}],"canvas_size":[562,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0555","image_path":"images/combination_0555.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0555_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0555_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0555_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":"combination_0555_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0555_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":555,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[594,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0556","image_path":"images/combination_0556.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0556_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0556_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0556_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0556_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0556_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":556,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[551,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0557","image_path":"images/combination_0557.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0557_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0557_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0557_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0557_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0557_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":557,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0558","image_path":"images/combination_0558.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0558_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0558_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_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":"C","question_id":"combination_0558_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0558_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":558,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3],[4,1],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_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],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[550,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0559","image_path":"images/combination_0559.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0559_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0559_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0559_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0559_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0559_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":559,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0560","image_path":"images/combination_0560.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0560_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0560_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0560_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":"combination_0560_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0560_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":560,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[587,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0561","image_path":"images/combination_0561.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0561_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0561_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0561_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":"combination_0561_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0561_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":561,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[597,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0562","image_path":"images/combination_0562.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0562_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0562_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0562_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":"combination_0562_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0562_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":562,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[583,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0563","image_path":"images/combination_0563.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0563_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0563_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0563_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":"combination_0563_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0563_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":563,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[568,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0564","image_path":"images/combination_0564.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0564_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0564_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0564_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0564_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0564_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":564,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[590,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0565","image_path":"images/combination_0565.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0565_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0565_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0565_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":"combination_0565_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0565_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":565,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[600,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0566","image_path":"images/combination_0566.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0566_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0566_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0566_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0566_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0566_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":566,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1],[4,2],[5,0],[5,1],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[559,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0567","image_path":"images/combination_0567.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0567_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0567_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0567_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0567_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0567_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":567,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[556,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0568","image_path":"images/combination_0568.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0568_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0568_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0568_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0568_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0568_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":568,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0569","image_path":"images/combination_0569.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0569_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0569_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0569_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0569_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0569_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":569,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0570","image_path":"images/combination_0570.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0570_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0570_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0570_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0570_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0570_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":570,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[559,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0571","image_path":"images/combination_0571.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0571_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0571_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0571_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":"combination_0571_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0571_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":571,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[563,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0572","image_path":"images/combination_0572.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0572_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0572_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0572_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0572_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0572_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":572,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0573","image_path":"images/combination_0573.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0573_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0573_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"D","question_id":"combination_0573_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0573_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":573,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[569,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0574","image_path":"images/combination_0574.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0574_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0574_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0574_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":"combination_0574_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0574_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":574,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[569,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0575","image_path":"images/combination_0575.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0575_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0575_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0575_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":"combination_0575_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0575_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":575,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[598,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0576","image_path":"images/combination_0576.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0576_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0576_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0576_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0576_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0576_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":576,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[1,5],[2,3],[2,4],[2,5],[2,6]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[575,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0577","image_path":"images/combination_0577.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0577_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0577_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0577_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0577_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0577_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":577,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0578","image_path":"images/combination_0578.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0578_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0578_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0578_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":"combination_0578_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0578_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":578,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0579","image_path":"images/combination_0579.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0579_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0579_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0579_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":"combination_0579_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0579_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":579,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0580","image_path":"images/combination_0580.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0580_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0580_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0580_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":"combination_0580_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0580_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":580,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[595,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0581","image_path":"images/combination_0581.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0581_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0581_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0581_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":"combination_0581_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0581_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":581,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[563,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0582","image_path":"images/combination_0582.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0582_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0582_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0582_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":"combination_0582_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0582_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":582,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0583","image_path":"images/combination_0583.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0583_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0583_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0583_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":"combination_0583_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0583_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":583,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[588,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0584","image_path":"images/combination_0584.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0584_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0584_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0584_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":"combination_0584_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0584_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":584,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[553,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0585","image_path":"images/combination_0585.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0585_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0585_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0585_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0585_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0585_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":585,"target_cell_count":7,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[597,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0586","image_path":"images/combination_0586.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0586_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0586_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0586_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":"combination_0586_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0586_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":586,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0587","image_path":"images/combination_0587.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0587_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0587_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_0587_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":"combination_0587_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0587_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":587,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[596,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0588","image_path":"images/combination_0588.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0588_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0588_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0588_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":"combination_0588_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0588_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":588,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[557,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0589","image_path":"images/combination_0589.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0589_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0589_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0589_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":"combination_0589_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0589_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":589,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[551,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0590","image_path":"images/combination_0590.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0590_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0590_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0590_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0590_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0590_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":590,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[585,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0591","image_path":"images/combination_0591.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0591_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0591_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0591_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0591_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0591_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":591,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[554,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0592","image_path":"images/combination_0592.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0592_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0592_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0592_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":"combination_0592_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0592_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":592,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[570,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0593","image_path":"images/combination_0593.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0593_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0593_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0593_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":"combination_0593_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0593_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":593,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[558,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0594","image_path":"images/combination_0594.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0594_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0594_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0594_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0594_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0594_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":594,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[572,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0595","image_path":"images/combination_0595.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0595_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0595_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0595_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":"combination_0595_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0595_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":595,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0596","image_path":"images/combination_0596.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0596_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0596_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0596_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0596_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0596_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":596,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[556,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0597","image_path":"images/combination_0597.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0597_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0597_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0597_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0597_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0597_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":597,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]]],"total_cell_count":9}],"canvas_size":[556,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0598","image_path":"images/combination_0598.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0598_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0598_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0598_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0598_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0598_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":598,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[595,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0599","image_path":"images/combination_0599.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0599_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0599_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0599_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0599_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0599_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":599,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[566,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0600","image_path":"images/combination_0600.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0600_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0600_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0600_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0600_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0600_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":600,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0],[1,0],[2,0]]],"total_cell_count":10}],"canvas_size":[562,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0601","image_path":"images/combination_0601.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0601_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0601_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0601_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":"combination_0601_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0601_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":601,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0602","image_path":"images/combination_0602.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0602_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0602_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0602_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0602_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0602_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":602,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[560,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0603","image_path":"images/combination_0603.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0603_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0603_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0603_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0603_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0603_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":603,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9}],"canvas_size":[554,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0604","image_path":"images/combination_0604.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0604_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0604_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0604_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":"combination_0604_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0604_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":604,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_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],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[561,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0605","image_path":"images/combination_0605.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0605_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0605_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0605_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":"combination_0605_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0605_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":605,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[597,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0606","image_path":"images/combination_0606.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0606_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0606_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0606_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":"combination_0606_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0606_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":606,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[594,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0607","image_path":"images/combination_0607.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0607_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0607_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_0607_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0607_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":607,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[558,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0608","image_path":"images/combination_0608.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0608_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0608_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0608_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0608_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0608_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":608,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0609","image_path":"images/combination_0609.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0609_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0609_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0609_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":"combination_0609_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0609_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":609,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[578,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0610","image_path":"images/combination_0610.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0610_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0610_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_0610_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0610_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":610,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0611","image_path":"images/combination_0611.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0611_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0611_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0611_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0611_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0611_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":611,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[564,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0612","image_path":"images/combination_0612.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0612_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0612_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0612_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0612_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0612_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":612,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[567,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0613","image_path":"images/combination_0613.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0613_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0613_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0613_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":"combination_0613_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0613_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":613,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[566,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0614","image_path":"images/combination_0614.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0614_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0614_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0614_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0614_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0614_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":614,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[564,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0615","image_path":"images/combination_0615.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0615_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0615_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0615_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0615_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0615_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":615,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[551,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0616","image_path":"images/combination_0616.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0616_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0616_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0616_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":"combination_0616_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0616_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":616,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[594,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0617","image_path":"images/combination_0617.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0617_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0617_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0617_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0617_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0617_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":617,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":7}],"canvas_size":[579,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0618","image_path":"images/combination_0618.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0618_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0618_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_0618_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0618_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":618,"target_cell_count":7,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[582,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0619","image_path":"images/combination_0619.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0619_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0619_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0619_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":"combination_0619_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0619_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":619,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"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],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":10}],"canvas_size":[564,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0620","image_path":"images/combination_0620.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0620_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0620_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0620_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0620_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0620_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":620,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,1],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3],[4,0],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,2],[3,1],[3,2],[3,3],[4,0],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0621","image_path":"images/combination_0621.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0621_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0621_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0621_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0621_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0621_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":621,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[568,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0622","image_path":"images/combination_0622.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0622_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0622_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0622_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0622_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0622_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":622,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0623","image_path":"images/combination_0623.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0623_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0623_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0623_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":"combination_0623_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0623_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":623,"target_cell_count":7,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[562,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0624","image_path":"images/combination_0624.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0624_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0624_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0624_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":"combination_0624_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0624_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":624,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10}],"canvas_size":[576,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0625","image_path":"images/combination_0625.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0625_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0625_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0625_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0625_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0625_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":625,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0626","image_path":"images/combination_0626.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0626_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0626_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0626_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0626_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0626_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":626,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[566,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0627","image_path":"images/combination_0627.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0627_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0627_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0627_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0627_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0627_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":627,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[575,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0628","image_path":"images/combination_0628.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0628_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0628_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0628_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":"combination_0628_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0628_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":628,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[553,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0629","image_path":"images/combination_0629.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0629_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0629_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0629_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0629_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0629_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":629,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,2],[2,1],[2,2],[2,3],[2,4],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]],"total_cell_count":9}],"canvas_size":[579,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0630","image_path":"images/combination_0630.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0630_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0630_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0630_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":"combination_0630_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0630_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":630,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[600,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0631","image_path":"images/combination_0631.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0631_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0631_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"D","question_id":"combination_0631_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0631_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":631,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[2,1],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0],[5,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[573,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0632","image_path":"images/combination_0632.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0632_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0632_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0632_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0632_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0632_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":632,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[552,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0633","image_path":"images/combination_0633.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0633_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0633_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0633_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0633_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0633_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":633,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[558,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0634","image_path":"images/combination_0634.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0634_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0634_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0634_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0634_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0634_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":634,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3],[4,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":10}],"canvas_size":[572,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0635","image_path":"images/combination_0635.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0635_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0635_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0635_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0635_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0635_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":635,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[562,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0636","image_path":"images/combination_0636.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0636_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0636_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0636_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":"combination_0636_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0636_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":636,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8}],"canvas_size":[581,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0637","image_path":"images/combination_0637.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0637_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0637_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0637_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":"combination_0637_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0637_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":637,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[590,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0638","image_path":"images/combination_0638.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0638_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0638_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0638_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0638_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0638_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":638,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[595,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0639","image_path":"images/combination_0639.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0639_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0639_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0639_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0639_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0639_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":639,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[551,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0640","image_path":"images/combination_0640.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0640_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0640_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0640_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0640_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0640_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":640,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[0,4],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3],[3,3],[3,4]],[[0,0]]],"total_cell_count":10}],"canvas_size":[574,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0641","image_path":"images/combination_0641.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0641_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0641_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0641_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":"combination_0641_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0641_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":641,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[592,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0642","image_path":"images/combination_0642.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0642_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0642_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0642_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0642_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0642_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":642,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]]],"total_cell_count":9}],"canvas_size":[585,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0643","image_path":"images/combination_0643.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0643_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0643_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0643_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":"combination_0643_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0643_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":643,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[581,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0644","image_path":"images/combination_0644.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0644_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0644_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0644_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":"combination_0644_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0644_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":644,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[562,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0645","image_path":"images/combination_0645.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0645_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0645_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0645_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":"combination_0645_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0645_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":645,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0646","image_path":"images/combination_0646.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0646_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0646_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0646_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":"combination_0646_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0646_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":646,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[592,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0647","image_path":"images/combination_0647.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0647_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0647_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0647_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":"combination_0647_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0647_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":647,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[591,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0648","image_path":"images/combination_0648.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0648_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0648_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0648_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0648_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0648_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":648,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2],[4,3],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0649","image_path":"images/combination_0649.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0649_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0649_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0649_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":"combination_0649_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0649_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":649,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[570,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0650","image_path":"images/combination_0650.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0650_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0650_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0650_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0650_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0650_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":650,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0651","image_path":"images/combination_0651.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0651_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0651_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0651_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0651_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0651_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":651,"target_cell_count":7,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[559,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0652","image_path":"images/combination_0652.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0652_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0652_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0652_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0652_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0652_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":652,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[597,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0653","image_path":"images/combination_0653.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0653_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0653_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0653_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0653_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0653_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":653,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0654","image_path":"images/combination_0654.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0654_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0654_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0654_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":"combination_0654_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0654_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":654,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":8}],"canvas_size":[552,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0655","image_path":"images/combination_0655.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0655_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0655_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0655_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":"combination_0655_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0655_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":655,"target_cell_count":8,"target_cells":[[0,3],[1,3],[2,0],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","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],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0656","image_path":"images/combination_0656.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0656_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0656_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0656_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0656_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0656_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":656,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[588,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0657","image_path":"images/combination_0657.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0657_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0657_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_0657_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0657_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":657,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[559,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0658","image_path":"images/combination_0658.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0658_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0658_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0658_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0658_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0658_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":658,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8}],"canvas_size":[596,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0659","image_path":"images/combination_0659.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0659_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0659_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"D","question_id":"combination_0659_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0659_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":659,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,4]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,4],[1,2],[1,3],[1,4]]],"total_cell_count":9}],"canvas_size":[551,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0660","image_path":"images/combination_0660.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0660_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0660_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0660_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0660_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0660_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":660,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,4],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0661","image_path":"images/combination_0661.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0661_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0661_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0661_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0661_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0661_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":661,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[590,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0662","image_path":"images/combination_0662.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0662_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0662_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0662_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":"combination_0662_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0662_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":662,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[2,0],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[594,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0663","image_path":"images/combination_0663.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0663_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0663_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0663_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":"combination_0663_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0663_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":663,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[600,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0664","image_path":"images/combination_0664.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0664_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0664_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0664_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0664_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0664_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":664,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[583,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0665","image_path":"images/combination_0665.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0665_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0665_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0665_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":"combination_0665_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0665_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":665,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[579,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0666","image_path":"images/combination_0666.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0666_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0666_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_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":"combination_0666_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0666_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":666,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8}],"canvas_size":[556,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0667","image_path":"images/combination_0667.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0667_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0667_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0667_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":"combination_0667_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0667_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":667,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0668","image_path":"images/combination_0668.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0668_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0668_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0668_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":"combination_0668_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0668_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":668,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10}],"canvas_size":[569,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0669","image_path":"images/combination_0669.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0669_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0669_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0669_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":"combination_0669_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0669_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":669,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[586,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0670","image_path":"images/combination_0670.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0670_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0670_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0670_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0670_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0670_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":670,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[587,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0671","image_path":"images/combination_0671.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0671_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0671_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0671_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":"combination_0671_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0671_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":671,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0672","image_path":"images/combination_0672.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0672_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0672_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0672_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0672_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0672_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":672,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[583,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0673","image_path":"images/combination_0673.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0673_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0673_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0673_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0673_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0673_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":673,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[575,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0674","image_path":"images/combination_0674.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0674_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0674_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0674_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0674_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0674_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":674,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[563,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0675","image_path":"images/combination_0675.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0675_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0675_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0675_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0675_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0675_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":675,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[551,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0676","image_path":"images/combination_0676.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0676_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0676_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0676_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":"combination_0676_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0676_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":676,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[590,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0677","image_path":"images/combination_0677.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0677_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0677_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0677_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":"combination_0677_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0677_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":677,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[557,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0678","image_path":"images/combination_0678.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0678_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0678_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0678_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":"combination_0678_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0678_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":678,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9}],"canvas_size":[591,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0679","image_path":"images/combination_0679.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0679_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0679_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0679_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0679_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0679_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":679,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3],[2,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[589,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0680","image_path":"images/combination_0680.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0680_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0680_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0680_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":"combination_0680_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0680_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":680,"target_cell_count":10,"target_cells":[[0,1],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[576,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0681","image_path":"images/combination_0681.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0681_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0681_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0681_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":"combination_0681_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0681_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":681,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[583,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0682","image_path":"images/combination_0682.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0682_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0682_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0682_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0682_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0682_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":682,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[575,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0683","image_path":"images/combination_0683.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0683_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0683_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0683_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0683_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0683_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":683,"target_cell_count":6,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[574,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0684","image_path":"images/combination_0684.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0684_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0684_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0684_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":"combination_0684_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0684_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":684,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[569,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0685","image_path":"images/combination_0685.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0685_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0685_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0685_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0685_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0685_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":685,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0686","image_path":"images/combination_0686.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0686_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0686_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0686_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0686_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0686_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":686,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[575,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0687","image_path":"images/combination_0687.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0687_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0687_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0687_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0687_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0687_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":687,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[597,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0688","image_path":"images/combination_0688.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0688_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0688_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0688_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":"combination_0688_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0688_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":688,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":8}],"canvas_size":[588,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0689","image_path":"images/combination_0689.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0689_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0689_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0689_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0689_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0689_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":689,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9}],"canvas_size":[570,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0690","image_path":"images/combination_0690.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0690_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0690_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0690_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0690_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0690_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":690,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[594,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0691","image_path":"images/combination_0691.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0691_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0691_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0691_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0691_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0691_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":691,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0692","image_path":"images/combination_0692.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0692_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0692_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0692_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0692_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0692_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":692,"target_cell_count":7,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[580,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0693","image_path":"images/combination_0693.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0693_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0693_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0693_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0693_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0693_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":693,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[594,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0694","image_path":"images/combination_0694.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0694_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0694_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0694_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":"combination_0694_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0694_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":694,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[571,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0695","image_path":"images/combination_0695.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0695_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0695_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0695_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":"combination_0695_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0695_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":695,"target_cell_count":7,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9}],"canvas_size":[560,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0696","image_path":"images/combination_0696.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0696_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0696_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0696_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":"combination_0696_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0696_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":696,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[558,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0697","image_path":"images/combination_0697.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0697_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0697_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0697_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":"combination_0697_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0697_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":697,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0698","image_path":"images/combination_0698.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0698_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0698_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0698_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0698_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0698_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":698,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"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]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0699","image_path":"images/combination_0699.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0699_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0699_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0699_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":"combination_0699_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0699_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":699,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0700","image_path":"images/combination_0700.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0700_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0700_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0700_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":"combination_0700_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0700_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":700,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[597,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0701","image_path":"images/combination_0701.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0701_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0701_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0701_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0701_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0701_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":701,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0702","image_path":"images/combination_0702.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0702_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0702_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0702_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":"combination_0702_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0702_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":702,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_0703","image_path":"images/combination_0703.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0703_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0703_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0703_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":"combination_0703_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0703_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":703,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[589,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0704","image_path":"images/combination_0704.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0704_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0704_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0704_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0704_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0704_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":704,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[2,4],[3,4],[3,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[599,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0705","image_path":"images/combination_0705.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0705_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0705_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0705_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0705_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0705_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":705,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[589,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0706","image_path":"images/combination_0706.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0706_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0706_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0706_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0706_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0706_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":706,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0707","image_path":"images/combination_0707.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0707_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0707_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0707_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":"combination_0707_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0707_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":707,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[557,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0708","image_path":"images/combination_0708.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0708_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0708_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0708_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0708_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0708_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":708,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_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],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[584,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0709","image_path":"images/combination_0709.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0709_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0709_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0709_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":"combination_0709_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0709_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":709,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0710","image_path":"images/combination_0710.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0710_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0710_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0710_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":"combination_0710_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0710_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":710,"target_cell_count":10,"target_cells":[[0,4],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]],"total_cell_count":9}],"canvas_size":[589,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0711","image_path":"images/combination_0711.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0711_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0711_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0711_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0711_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0711_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":711,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0712","image_path":"images/combination_0712.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0712_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0712_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0712_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0712_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0712_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":712,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[574,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0713","image_path":"images/combination_0713.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0713_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0713_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0713_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":"combination_0713_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0713_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":713,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":6}],"canvas_size":[599,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0714","image_path":"images/combination_0714.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0714_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0714_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0714_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":"combination_0714_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0714_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":714,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[582,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0715","image_path":"images/combination_0715.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0715_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0715_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0715_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":"combination_0715_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0715_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":715,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0716","image_path":"images/combination_0716.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0716_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0716_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0716_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":"combination_0716_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0716_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":716,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0717","image_path":"images/combination_0717.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0717_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0717_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0717_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":"combination_0717_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0717_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":717,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[566,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0718","image_path":"images/combination_0718.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0718_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0718_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0718_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0718_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0718_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":718,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":5}],"canvas_size":[567,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0719","image_path":"images/combination_0719.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0719_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0719_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0719_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":"combination_0719_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0719_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":719,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[597,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0720","image_path":"images/combination_0720.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0720_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0720_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0720_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0720_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0720_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":720,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,6],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[1,6]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[559,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0721","image_path":"images/combination_0721.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0721_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0721_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0721_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":"combination_0721_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0721_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":721,"target_cell_count":9,"target_cells":[[0,3],[0,6],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7}],"canvas_size":[589,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0722","image_path":"images/combination_0722.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0722_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0722_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0722_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":"combination_0722_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0722_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":722,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,4],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0723","image_path":"images/combination_0723.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0723_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0723_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0723_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0723_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0723_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":723,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0724","image_path":"images/combination_0724.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0724_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0724_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0724_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0724_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0724_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":724,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[555,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0725","image_path":"images/combination_0725.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0725_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0725_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0725_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0725_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0725_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":725,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[566,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0726","image_path":"images/combination_0726.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0726_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0726_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0726_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":"combination_0726_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0726_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":726,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0727","image_path":"images/combination_0727.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0727_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0727_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0727_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0727_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0727_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":727,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[4,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2],[4,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[552,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0728","image_path":"images/combination_0728.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0728_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0728_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0728_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0728_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0728_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":728,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[594,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0729","image_path":"images/combination_0729.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0729_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0729_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_0729_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0729_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":729,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[569,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0730","image_path":"images/combination_0730.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0730_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0730_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_0730_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":"combination_0730_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0730_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":730,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[596,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0731","image_path":"images/combination_0731.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0731_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0731_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0731_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":"combination_0731_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0731_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":731,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0732","image_path":"images/combination_0732.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0732_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0732_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0732_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":"combination_0732_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0732_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":732,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0733","image_path":"images/combination_0733.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0733_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0733_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0733_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0733_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0733_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":733,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[593,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0734","image_path":"images/combination_0734.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0734_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0734_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0734_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0734_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0734_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":734,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6}],"canvas_size":[577,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0735","image_path":"images/combination_0735.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0735_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0735_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0735_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":"combination_0735_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0735_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":735,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0736","image_path":"images/combination_0736.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0736_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0736_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0736_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0736_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0736_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":736,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[550,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0737","image_path":"images/combination_0737.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0737_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0737_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0737_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0737_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0737_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":737,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[560,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0738","image_path":"images/combination_0738.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0738_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0738_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0738_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0738_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0738_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":738,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8}],"canvas_size":[562,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0739","image_path":"images/combination_0739.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0739_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0739_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0739_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0739_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0739_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":739,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[586,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0740","image_path":"images/combination_0740.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0740_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0740_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0740_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0740_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0740_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":740,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[564,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0741","image_path":"images/combination_0741.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0741_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0741_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0741_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0741_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0741_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":741,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[576,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0742","image_path":"images/combination_0742.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0742_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0742_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0742_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":"combination_0742_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0742_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":742,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[0,4],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[0,4],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4],[3,3],[3,4]]],"total_cell_count":10}],"canvas_size":[594,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0743","image_path":"images/combination_0743.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0743_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0743_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0743_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0743_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0743_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":743,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[569,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0744","image_path":"images/combination_0744.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0744_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0744_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0744_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0744_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0744_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":744,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10}],"canvas_size":[564,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0745","image_path":"images/combination_0745.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0745_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0745_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0745_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":"combination_0745_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0745_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":745,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[577,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0746","image_path":"images/combination_0746.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0746_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0746_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_0746_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0746_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":746,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":6}],"canvas_size":[569,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0747","image_path":"images/combination_0747.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0747_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0747_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0747_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0747_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0747_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":747,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0748","image_path":"images/combination_0748.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0748_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0748_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0748_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":"combination_0748_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0748_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":748,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[598,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0749","image_path":"images/combination_0749.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0749_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0749_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0749_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0749_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0749_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":749,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[570,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0750","image_path":"images/combination_0750.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0750_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0750_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0750_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0750_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0750_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":750,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[598,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0751","image_path":"images/combination_0751.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0751_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0751_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0751_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":"combination_0751_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0751_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":751,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0752","image_path":"images/combination_0752.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0752_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0752_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0752_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":"combination_0752_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0752_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":752,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[598,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0753","image_path":"images/combination_0753.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0753_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0753_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0753_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0753_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0753_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":753,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0754","image_path":"images/combination_0754.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0754_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0754_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0754_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":"combination_0754_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0754_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":754,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[583,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0755","image_path":"images/combination_0755.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0755_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0755_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0755_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":"combination_0755_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0755_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":755,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[579,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0756","image_path":"images/combination_0756.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0756_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0756_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0756_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":"combination_0756_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0756_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":756,"target_cell_count":10,"target_cells":[[0,4],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[575,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0757","image_path":"images/combination_0757.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0757_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0757_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0757_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0757_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0757_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":757,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[571,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0758","image_path":"images/combination_0758.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0758_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0758_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0758_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0758_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0758_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":758,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[553,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0759","image_path":"images/combination_0759.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0759_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0759_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0759_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0759_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0759_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":759,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[558,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0760","image_path":"images/combination_0760.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0760_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0760_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0760_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":"combination_0760_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0760_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":760,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[564,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0761","image_path":"images/combination_0761.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0761_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0761_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0761_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":"combination_0761_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0761_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":761,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[590,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0762","image_path":"images/combination_0762.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0762_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0762_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0762_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":"combination_0762_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0762_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":762,"target_cell_count":7,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9}],"canvas_size":[589,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0763","image_path":"images/combination_0763.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0763_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0763_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0763_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":"combination_0763_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0763_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":763,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[592,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0764","image_path":"images/combination_0764.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0764_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0764_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0764_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":"combination_0764_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0764_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":764,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0765","image_path":"images/combination_0765.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0765_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0765_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0765_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":"combination_0765_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0765_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":765,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0766","image_path":"images/combination_0766.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0766_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0766_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0766_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0766_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0766_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":766,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0767","image_path":"images/combination_0767.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0767_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0767_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0767_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0767_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0767_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":767,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[555,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0768","image_path":"images/combination_0768.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0768_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0768_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0768_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0768_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0768_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":768,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[550,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0769","image_path":"images/combination_0769.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0769_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0769_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0769_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0769_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0769_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":769,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0770","image_path":"images/combination_0770.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0770_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0770_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0770_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":"combination_0770_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0770_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":770,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[574,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0771","image_path":"images/combination_0771.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0771_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0771_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0771_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0771_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0771_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":771,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0772","image_path":"images/combination_0772.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0772_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0772_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0772_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":"combination_0772_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0772_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":772,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[561,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0773","image_path":"images/combination_0773.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0773_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0773_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0773_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0773_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0773_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":773,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[569,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0774","image_path":"images/combination_0774.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0774_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0774_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0774_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":"combination_0774_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0774_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":774,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0775","image_path":"images/combination_0775.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0775_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0775_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0775_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":"combination_0775_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0775_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":775,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[578,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0776","image_path":"images/combination_0776.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0776_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0776_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0776_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":"combination_0776_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0776_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":776,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[5,1],[6,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[564,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0777","image_path":"images/combination_0777.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0777_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0777_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0777_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":"combination_0777_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0777_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":777,"target_cell_count":9,"target_cells":[[0,3],[0,4],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0778","image_path":"images/combination_0778.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0778_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0778_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0778_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":"combination_0778_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0778_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":778,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[586,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0779","image_path":"images/combination_0779.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0779_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0779_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0779_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":"combination_0779_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0779_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":779,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0780","image_path":"images/combination_0780.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0780_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0780_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0780_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0780_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0780_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":780,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[563,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0781","image_path":"images/combination_0781.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0781_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0781_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0781_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":"combination_0781_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0781_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":781,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[2,2],[3,1],[4,0],[4,1]]],"total_cell_count":8}],"canvas_size":[592,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0782","image_path":"images/combination_0782.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0782_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0782_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0782_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":"combination_0782_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0782_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":782,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0783","image_path":"images/combination_0783.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0783_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0783_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0783_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":"combination_0783_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0783_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":783,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[577,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0784","image_path":"images/combination_0784.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0784_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0784_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0784_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0784_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0784_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":784,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[582,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0785","image_path":"images/combination_0785.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0785_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0785_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0785_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0785_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0785_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":785,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[573,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0786","image_path":"images/combination_0786.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0786_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0786_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0786_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":"combination_0786_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0786_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":786,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[2,2],[2,3],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[569,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0787","image_path":"images/combination_0787.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0787_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0787_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0787_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":"combination_0787_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0787_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":787,"target_cell_count":9,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0788","image_path":"images/combination_0788.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0788_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0788_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0788_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0788_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0788_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":788,"target_cell_count":6,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[580,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0789","image_path":"images/combination_0789.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0789_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0789_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0789_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":"combination_0789_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0789_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":789,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[590,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0790","image_path":"images/combination_0790.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0790_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0790_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_0790_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0790_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":790,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[593,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0791","image_path":"images/combination_0791.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0791_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0791_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0791_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":"combination_0791_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0791_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":791,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,3],[1,4],[2,0],[2,1],[2,4],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[586,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0792","image_path":"images/combination_0792.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0792_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0792_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0792_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":"combination_0792_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0792_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":792,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[589,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0793","image_path":"images/combination_0793.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0793_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0793_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0793_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0793_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0793_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":793,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0794","image_path":"images/combination_0794.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0794_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0794_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0794_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":"combination_0794_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0794_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":794,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_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],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[575,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0795","image_path":"images/combination_0795.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0795_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0795_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0795_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":"combination_0795_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0795_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":795,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0796","image_path":"images/combination_0796.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0796_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0796_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0796_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0796_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0796_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":796,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[588,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0797","image_path":"images/combination_0797.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0797_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0797_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0797_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":"combination_0797_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0797_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":797,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0798","image_path":"images/combination_0798.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0798_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0798_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0798_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":"combination_0798_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0798_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":798,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0799","image_path":"images/combination_0799.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0799_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0799_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0799_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0799_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0799_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":799,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[592,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0800","image_path":"images/combination_0800.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0800_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0800_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0800_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0800_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0800_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":800,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0801","image_path":"images/combination_0801.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0801_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0801_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0801_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0801_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0801_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":801,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[585,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0802","image_path":"images/combination_0802.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0802_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0802_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0802_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":"combination_0802_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0802_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":802,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0803","image_path":"images/combination_0803.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0803_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0803_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0803_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0803_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0803_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":803,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[580,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0804","image_path":"images/combination_0804.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0804_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0804_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0804_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0804_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0804_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":804,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0805","image_path":"images/combination_0805.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0805_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0805_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0805_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0805_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0805_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":805,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]]],"total_cell_count":10}],"canvas_size":[579,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0806","image_path":"images/combination_0806.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0806_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0806_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0806_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":"combination_0806_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0806_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":806,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[573,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0807","image_path":"images/combination_0807.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0807_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0807_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0807_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":"combination_0807_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0807_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":807,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8}],"canvas_size":[573,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0808","image_path":"images/combination_0808.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0808_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0808_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0808_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0808_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0808_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":808,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[553,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0809","image_path":"images/combination_0809.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0809_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0809_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0809_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":"combination_0809_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0809_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":809,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[595,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0810","image_path":"images/combination_0810.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0810_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0810_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0810_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0810_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0810_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":810,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3],[2,4],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[555,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0811","image_path":"images/combination_0811.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0811_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0811_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0811_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0811_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0811_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":811,"target_cell_count":10,"target_cells":[[0,3],[0,5],[1,3],[1,4],[1,5],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[552,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0812","image_path":"images/combination_0812.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0812_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0812_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0812_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0812_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0812_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":812,"target_cell_count":10,"target_cells":[[0,4],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[1,1],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[558,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0813","image_path":"images/combination_0813.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0813_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0813_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0813_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0813_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0813_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":813,"target_cell_count":10,"target_cells":[[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,2]]],"total_cell_count":7}],"canvas_size":[588,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0814","image_path":"images/combination_0814.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0814_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0814_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0814_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0814_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0814_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":814,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[550,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0815","image_path":"images/combination_0815.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0815_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0815_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0815_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0815_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0815_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":815,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0816","image_path":"images/combination_0816.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0816_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0816_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0816_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":"combination_0816_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0816_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":816,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[558,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0817","image_path":"images/combination_0817.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0817_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0817_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0817_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":"combination_0817_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0817_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":817,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[580,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0818","image_path":"images/combination_0818.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0818_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0818_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0818_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":"combination_0818_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0818_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":818,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6}],"canvas_size":[573,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0819","image_path":"images/combination_0819.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0819_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0819_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0819_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":"combination_0819_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0819_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":819,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[563,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0820","image_path":"images/combination_0820.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0820_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0820_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_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":"A","question_id":"combination_0820_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0820_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":820,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[586,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0821","image_path":"images/combination_0821.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0821_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0821_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0821_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":"combination_0821_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0821_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":821,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0822","image_path":"images/combination_0822.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0822_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0822_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0822_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":"combination_0822_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0822_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":822,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[571,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0823","image_path":"images/combination_0823.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0823_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0823_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0823_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":"combination_0823_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0823_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":823,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[591,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0824","image_path":"images/combination_0824.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0824_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0824_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0824_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0824_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0824_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":824,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[567,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0825","image_path":"images/combination_0825.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0825_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0825_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0825_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0825_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0825_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":825,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[585,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0826","image_path":"images/combination_0826.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0826_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0826_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0826_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0826_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0826_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":826,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[572,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0827","image_path":"images/combination_0827.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0827_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0827_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0827_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":"combination_0827_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0827_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":827,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[562,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0828","image_path":"images/combination_0828.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0828_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0828_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0828_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0828_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0828_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":828,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[563,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0829","image_path":"images/combination_0829.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0829_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0829_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0829_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":"combination_0829_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0829_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":829,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0830","image_path":"images/combination_0830.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0830_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0830_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0830_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":"combination_0830_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0830_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":830,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[560,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0831","image_path":"images/combination_0831.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0831_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0831_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_0831_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":"combination_0831_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0831_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":831,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0832","image_path":"images/combination_0832.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0832_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0832_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0832_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":"combination_0832_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0832_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":832,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0833","image_path":"images/combination_0833.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0833_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0833_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0833_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0833_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0833_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":833,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0834","image_path":"images/combination_0834.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0834_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0834_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0834_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":"combination_0834_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0834_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":834,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[589,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0835","image_path":"images/combination_0835.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0835_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0835_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0835_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":"combination_0835_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0835_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":835,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[3,2],[3,3],[4,0],[4,1],[4,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0836","image_path":"images/combination_0836.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0836_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0836_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0836_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":"combination_0836_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0836_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":836,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,1],[3,2],[3,3],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9}],"canvas_size":[585,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0837","image_path":"images/combination_0837.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0837_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0837_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0837_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":"combination_0837_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0837_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":837,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":8}],"canvas_size":[582,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0838","image_path":"images/combination_0838.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0838_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0838_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0838_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0838_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0838_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":838,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5}],"canvas_size":[589,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0839","image_path":"images/combination_0839.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0839_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0839_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0839_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":"combination_0839_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0839_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":839,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0840","image_path":"images/combination_0840.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0840_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0840_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0840_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0840_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0840_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":840,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[586,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0841","image_path":"images/combination_0841.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0841_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0841_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0841_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0841_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0841_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":841,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[554,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0842","image_path":"images/combination_0842.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0842_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0842_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0842_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0842_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0842_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":842,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[592,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0843","image_path":"images/combination_0843.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0843_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0843_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0843_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":"combination_0843_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0843_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":843,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[591,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0844","image_path":"images/combination_0844.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0844_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0844_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0844_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":"combination_0844_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0844_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":844,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0845","image_path":"images/combination_0845.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0845_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0845_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0845_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":"combination_0845_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0845_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":845,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]]],"total_cell_count":9}],"canvas_size":[556,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0846","image_path":"images/combination_0846.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0846_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0846_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0846_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":"combination_0846_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0846_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":846,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0847","image_path":"images/combination_0847.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0847_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0847_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0847_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":"combination_0847_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0847_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":847,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0848","image_path":"images/combination_0848.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0848_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0848_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0848_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":"combination_0848_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0848_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":848,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[550,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0849","image_path":"images/combination_0849.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0849_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0849_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0849_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":"combination_0849_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0849_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":849,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6}],"canvas_size":[581,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0850","image_path":"images/combination_0850.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0850_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0850_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0850_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0850_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0850_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":850,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0851","image_path":"images/combination_0851.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0851_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0851_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0851_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0851_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0851_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":851,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[600,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0852","image_path":"images/combination_0852.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0852_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0852_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0852_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":"combination_0852_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0852_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":852,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[575,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0853","image_path":"images/combination_0853.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0853_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0853_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0853_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":"combination_0853_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0853_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":853,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[4,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[598,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0854","image_path":"images/combination_0854.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0854_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0854_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0854_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":"combination_0854_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0854_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":854,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7}],"canvas_size":[565,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0855","image_path":"images/combination_0855.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0855_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0855_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0855_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":"combination_0855_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0855_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":855,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[563,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0856","image_path":"images/combination_0856.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0856_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0856_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0856_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":"combination_0856_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0856_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":856,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[580,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0857","image_path":"images/combination_0857.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0857_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0857_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_0857_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0857_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":857,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[583,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0858","image_path":"images/combination_0858.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0858_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0858_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0858_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":"combination_0858_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0858_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":858,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[586,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0859","image_path":"images/combination_0859.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0859_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0859_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0859_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0859_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0859_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":859,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[558,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0860","image_path":"images/combination_0860.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0860_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0860_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0860_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0860_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0860_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":860,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[578,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0861","image_path":"images/combination_0861.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0861_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0861_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0861_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":"combination_0861_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0861_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":861,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[586,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0862","image_path":"images/combination_0862.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0862_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0862_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0862_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0862_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0862_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":862,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[587,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0863","image_path":"images/combination_0863.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0863_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0863_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0863_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":"combination_0863_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0863_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":863,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6}],"canvas_size":[569,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0864","image_path":"images/combination_0864.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0864_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0864_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0864_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0864_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0864_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":864,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[575,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0865","image_path":"images/combination_0865.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0865_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0865_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0865_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0865_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0865_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":865,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[557,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0866","image_path":"images/combination_0866.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0866_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0866_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0866_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":"combination_0866_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0866_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":866,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[599,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0867","image_path":"images/combination_0867.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0867_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0867_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_0867_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":"combination_0867_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0867_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":867,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[575,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0868","image_path":"images/combination_0868.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0868_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0868_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_0868_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":"combination_0868_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0868_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":868,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[576,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0869","image_path":"images/combination_0869.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0869_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0869_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0869_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0869_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0869_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":869,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[565,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0870","image_path":"images/combination_0870.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0870_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0870_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0870_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0870_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0870_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":870,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[572,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0871","image_path":"images/combination_0871.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0871_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0871_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0871_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0871_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0871_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":871,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0872","image_path":"images/combination_0872.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0872_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0872_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0872_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":"combination_0872_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0872_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":872,"target_cell_count":7,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[559,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0873","image_path":"images/combination_0873.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0873_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0873_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0873_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0873_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0873_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":873,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[583,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0874","image_path":"images/combination_0874.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0874_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0874_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0874_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":"combination_0874_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0874_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":874,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[582,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0875","image_path":"images/combination_0875.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0875_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0875_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0875_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0875_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0875_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":875,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":8}],"canvas_size":[595,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0876","image_path":"images/combination_0876.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0876_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0876_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0876_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0876_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0876_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":876,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[564,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0877","image_path":"images/combination_0877.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0877_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0877_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0877_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":"combination_0877_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0877_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":877,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7}],"canvas_size":[584,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0878","image_path":"images/combination_0878.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0878_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0878_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0878_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0878_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0878_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":878,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[554,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0879","image_path":"images/combination_0879.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0879_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0879_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0879_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":"combination_0879_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0879_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":879,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[556,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0880","image_path":"images/combination_0880.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0880_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0880_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0880_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":"combination_0880_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0880_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":880,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0881","image_path":"images/combination_0881.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0881_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0881_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0881_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0881_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0881_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":881,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[550,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0882","image_path":"images/combination_0882.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0882_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0882_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0882_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0882_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0882_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":882,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7}],"canvas_size":[585,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0883","image_path":"images/combination_0883.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0883_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0883_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0883_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0883_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0883_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":883,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0884","image_path":"images/combination_0884.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0884_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0884_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0884_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":"combination_0884_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0884_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":884,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[573,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0885","image_path":"images/combination_0885.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0885_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0885_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0885_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":"combination_0885_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0885_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":885,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0886","image_path":"images/combination_0886.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0886_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0886_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0886_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":"combination_0886_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0886_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":886,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[581,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0887","image_path":"images/combination_0887.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0887_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0887_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0887_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0887_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0887_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":887,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[555,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0888","image_path":"images/combination_0888.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0888_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0888_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0888_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0888_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0888_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":888,"target_cell_count":10,"target_cells":[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[590,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0889","image_path":"images/combination_0889.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0889_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0889_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0889_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":"combination_0889_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0889_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":889,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8}],"canvas_size":[553,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0890","image_path":"images/combination_0890.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0890_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0890_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0890_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":"combination_0890_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0890_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":890,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":8}],"canvas_size":[590,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0891","image_path":"images/combination_0891.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0891_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0891_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0891_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0891_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0891_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":891,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":8}],"canvas_size":[564,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0892","image_path":"images/combination_0892.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0892_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0892_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0892_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":"combination_0892_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0892_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":892,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[582,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0893","image_path":"images/combination_0893.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0893_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0893_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0893_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":"combination_0893_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0893_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":893,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[578,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0894","image_path":"images/combination_0894.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0894_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0894_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0894_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0894_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0894_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":894,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0895","image_path":"images/combination_0895.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0895_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0895_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0895_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0895_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0895_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":895,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[562,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0896","image_path":"images/combination_0896.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0896_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0896_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0896_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":"combination_0896_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0896_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":896,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[553,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0897","image_path":"images/combination_0897.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0897_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0897_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0897_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0897_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0897_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":897,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[576,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0898","image_path":"images/combination_0898.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0898_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0898_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0898_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":"combination_0898_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0898_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":898,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[558,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0899","image_path":"images/combination_0899.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0899_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0899_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0899_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0899_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0899_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":899,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[1,5],[2,4],[2,5],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[589,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0900","image_path":"images/combination_0900.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0900_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0900_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0900_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":"combination_0900_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0900_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":900,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[577,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0901","image_path":"images/combination_0901.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0901_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0901_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0901_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0901_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0901_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":901,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]]],"total_cell_count":9}],"canvas_size":[567,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0902","image_path":"images/combination_0902.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0902_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0902_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0902_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":"combination_0902_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0902_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":902,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[552,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0903","image_path":"images/combination_0903.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0903_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0903_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0903_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":"combination_0903_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0903_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":903,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0904","image_path":"images/combination_0904.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0904_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0904_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0904_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0904_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0904_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":904,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0905","image_path":"images/combination_0905.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0905_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0905_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0905_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0905_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0905_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":905,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0906","image_path":"images/combination_0906.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0906_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0906_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0906_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0906_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0906_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":906,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":5}],"canvas_size":[594,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0907","image_path":"images/combination_0907.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0907_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0907_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_0907_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0907_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":907,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_0908","image_path":"images/combination_0908.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0908_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0908_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0908_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":"combination_0908_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0908_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":908,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[563,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0909","image_path":"images/combination_0909.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0909_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0909_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0909_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":"combination_0909_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0909_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":909,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[589,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0910","image_path":"images/combination_0910.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0910_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0910_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0910_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":"combination_0910_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0910_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":910,"target_cell_count":9,"target_cells":[[0,4],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[579,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0911","image_path":"images/combination_0911.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0911_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0911_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0911_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0911_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0911_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":911,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[583,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0912","image_path":"images/combination_0912.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0912_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0912_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0912_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0912_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0912_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":912,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0913","image_path":"images/combination_0913.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0913_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0913_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0913_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":"combination_0913_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0913_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":913,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[553,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0914","image_path":"images/combination_0914.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0914_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0914_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0914_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0914_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0914_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":914,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0915","image_path":"images/combination_0915.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0915_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0915_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0915_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0915_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0915_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":915,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[593,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0916","image_path":"images/combination_0916.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0916_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0916_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0916_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":"combination_0916_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0916_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":916,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[598,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0917","image_path":"images/combination_0917.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0917_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0917_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0917_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":"combination_0917_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0917_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":917,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[4,0],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[4,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[595,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0918","image_path":"images/combination_0918.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0918_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0918_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0918_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0918_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0918_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":918,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[593,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0919","image_path":"images/combination_0919.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0919_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0919_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0919_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":"combination_0919_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0919_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":919,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[588,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0920","image_path":"images/combination_0920.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0920_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0920_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0920_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":"combination_0920_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0920_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":920,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0921","image_path":"images/combination_0921.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0921_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0921_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0921_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":"combination_0921_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0921_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":921,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[553,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0922","image_path":"images/combination_0922.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0922_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0922_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0922_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0922_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0922_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":922,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[580,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0923","image_path":"images/combination_0923.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0923_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0923_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0923_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0923_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0923_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":923,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,1],[3,2],[3,3],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0924","image_path":"images/combination_0924.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0924_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0924_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0924_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":"combination_0924_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0924_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":924,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[555,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0925","image_path":"images/combination_0925.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0925_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0925_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0925_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0925_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0925_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":925,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[591,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0926","image_path":"images/combination_0926.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0926_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0926_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_0926_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0926_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":926,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[590,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0927","image_path":"images/combination_0927.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0927_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0927_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0927_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0927_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0927_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":927,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[569,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0928","image_path":"images/combination_0928.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0928_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0928_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0928_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0928_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0928_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":928,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[562,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0929","image_path":"images/combination_0929.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0929_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0929_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0929_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0929_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0929_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":929,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0930","image_path":"images/combination_0930.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0930_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0930_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0930_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":"combination_0930_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0930_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":930,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[577,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0931","image_path":"images/combination_0931.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0931_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0931_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0931_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0931_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0931_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":931,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[583,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0932","image_path":"images/combination_0932.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0932_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0932_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0932_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0932_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0932_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":932,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[583,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0933","image_path":"images/combination_0933.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0933_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0933_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0933_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":"combination_0933_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0933_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":933,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0934","image_path":"images/combination_0934.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0934_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0934_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0934_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0934_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0934_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":934,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[593,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0935","image_path":"images/combination_0935.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0935_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0935_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0935_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":"combination_0935_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0935_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":935,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_0936","image_path":"images/combination_0936.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0936_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0936_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0936_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0936_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0936_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":936,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5}],"canvas_size":[584,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0937","image_path":"images/combination_0937.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0937_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0937_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0937_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0937_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0937_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":937,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3],[2,4]]],"total_cell_count":8}],"canvas_size":[578,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0938","image_path":"images/combination_0938.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0938_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0938_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0938_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":"combination_0938_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0938_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":938,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[556,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0939","image_path":"images/combination_0939.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0939_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0939_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0939_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0939_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0939_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":939,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[572,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0940","image_path":"images/combination_0940.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0940_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0940_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0940_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0940_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0940_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":940,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[572,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0941","image_path":"images/combination_0941.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0941_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0941_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0941_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":"combination_0941_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0941_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":941,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[575,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0942","image_path":"images/combination_0942.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0942_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0942_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0942_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":"combination_0942_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0942_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":942,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":10}],"canvas_size":[584,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_0943","image_path":"images/combination_0943.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0943_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0943_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0943_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":"combination_0943_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0943_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":943,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_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],[0,1],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0944","image_path":"images/combination_0944.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0944_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0944_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0944_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0944_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0944_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":944,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[577,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0945","image_path":"images/combination_0945.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0945_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0945_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0945_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":"combination_0945_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0945_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":945,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]]],"total_cell_count":8}],"canvas_size":[552,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0946","image_path":"images/combination_0946.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0946_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0946_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0946_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0946_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0946_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":946,"target_cell_count":8,"target_cells":[[0,3],[1,3],[2,3],[3,0],[3,1],[3,2],[3,3],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4]]],"total_cell_count":8}],"canvas_size":[562,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0947","image_path":"images/combination_0947.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0947_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0947_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0947_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0947_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0947_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":947,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0948","image_path":"images/combination_0948.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0948_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0948_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0948_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":"combination_0948_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0948_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":948,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[4,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_0949","image_path":"images/combination_0949.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0949_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0949_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0949_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":"combination_0949_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0949_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":949,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[563,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0950","image_path":"images/combination_0950.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0950_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0950_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0950_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0950_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0950_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":950,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[598,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0951","image_path":"images/combination_0951.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0951_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0951_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0951_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":"combination_0951_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0951_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":951,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[557,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0952","image_path":"images/combination_0952.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0952_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0952_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0952_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":"combination_0952_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0952_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":952,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[550,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0953","image_path":"images/combination_0953.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0953_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0953_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0953_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0953_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0953_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":953,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[561,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0954","image_path":"images/combination_0954.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0954_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0954_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0954_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0954_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0954_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":954,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0955","image_path":"images/combination_0955.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0955_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0955_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0955_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":"combination_0955_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0955_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":955,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[593,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0956","image_path":"images/combination_0956.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0956_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0956_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_0956_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":"combination_0956_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0956_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":956,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[579,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0957","image_path":"images/combination_0957.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0957_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0957_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0957_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0957_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0957_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":957,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0958","image_path":"images/combination_0958.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0958_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0958_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0958_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0958_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0958_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":958,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0959","image_path":"images/combination_0959.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0959_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0959_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0959_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0959_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0959_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":959,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[574,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0960","image_path":"images/combination_0960.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0960_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0960_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_0960_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0960_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":960,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[591,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0961","image_path":"images/combination_0961.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0961_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0961_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_0961_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":"combination_0961_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0961_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":961,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[566,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_0962","image_path":"images/combination_0962.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0962_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0962_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_0962_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0962_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":962,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2],[3,3],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":7}],"canvas_size":[584,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_0963","image_path":"images/combination_0963.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0963_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0963_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_0963_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":"combination_0963_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0963_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":963,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[600,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_0964","image_path":"images/combination_0964.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_0964_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0964_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0964_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0964_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0964_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":964,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8}],"canvas_size":[564,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0965","image_path":"images/combination_0965.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0965_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0965_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0965_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0965_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0965_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":965,"target_cell_count":8,"target_cells":[[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[552,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0966","image_path":"images/combination_0966.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0966_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0966_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0966_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0966_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0966_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":966,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0967","image_path":"images/combination_0967.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0967_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0967_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0967_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":"combination_0967_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0967_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":967,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0],[4,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]]],"total_cell_count":10}],"canvas_size":[556,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0968","image_path":"images/combination_0968.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0968_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0968_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0968_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0968_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0968_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":968,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":10}],"canvas_size":[574,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0969","image_path":"images/combination_0969.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0969_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0969_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0969_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0969_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0969_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":969,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0970","image_path":"images/combination_0970.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0970_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0970_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0970_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0970_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0970_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":970,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[566,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0971","image_path":"images/combination_0971.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0971_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0971_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0971_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":"combination_0971_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0971_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":971,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0972","image_path":"images/combination_0972.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0972_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0972_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0972_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0972_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0972_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":972,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[559,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0973","image_path":"images/combination_0973.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0973_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0973_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0973_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":"combination_0973_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0973_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":973,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[571,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0974","image_path":"images/combination_0974.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0974_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0974_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0974_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0974_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0974_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":974,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":6}],"canvas_size":[581,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0975","image_path":"images/combination_0975.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0975_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0975_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_0975_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0975_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0975_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":975,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[571,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0976","image_path":"images/combination_0976.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0976_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0976_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0976_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0976_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0976_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":976,"target_cell_count":7,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[590,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0977","image_path":"images/combination_0977.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0977_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0977_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0977_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0977_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0977_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":977,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[587,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_0978","image_path":"images/combination_0978.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0978_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0978_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0978_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":"combination_0978_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0978_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":978,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0979","image_path":"images/combination_0979.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0979_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0979_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0979_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":"combination_0979_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0979_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":979,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[577,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0980","image_path":"images/combination_0980.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0980_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0980_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0980_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":"combination_0980_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0980_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":980,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[564,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0981","image_path":"images/combination_0981.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0981_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0981_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0981_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0981_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0981_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":981,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[582,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0982","image_path":"images/combination_0982.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0982_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0982_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0982_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":"combination_0982_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0982_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":982,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[592,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0983","image_path":"images/combination_0983.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0983_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0983_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_0983_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0983_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_0983_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":983,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[596,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0984","image_path":"images/combination_0984.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0984_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0984_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0984_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_0984_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0984_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":984,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[571,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0985","image_path":"images/combination_0985.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0985_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0985_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0985_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0985_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0985_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":985,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[4,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[557,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0986","image_path":"images/combination_0986.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0986_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0986_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_0986_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":"combination_0986_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0986_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":986,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10}],"canvas_size":[584,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_0987","image_path":"images/combination_0987.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0987_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0987_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0987_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0987_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0987_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":987,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0988","image_path":"images/combination_0988.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0988_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0988_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0988_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0988_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0988_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":988,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[555,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0989","image_path":"images/combination_0989.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0989_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0989_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0989_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0989_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0989_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":989,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1],[4,0],[4,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[582,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_0990","image_path":"images/combination_0990.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0990_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0990_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_0990_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":"combination_0990_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0990_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":990,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[559,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0991","image_path":"images/combination_0991.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0991_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0991_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0991_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_0991_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0991_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":991,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[562,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0992","image_path":"images/combination_0992.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0992_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0992_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_0992_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":"combination_0992_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0992_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":992,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0993","image_path":"images/combination_0993.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0993_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0993_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_0993_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0993_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0993_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":993,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[558,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0994","image_path":"images/combination_0994.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0994_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0994_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_0994_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":"combination_0994_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0994_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":994,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[561,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_0995","image_path":"images/combination_0995.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0995_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0995_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_0995_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":"combination_0995_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0995_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":995,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[578,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_0996","image_path":"images/combination_0996.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_0996_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_0996_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0996_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0996_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_0996_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":996,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[579,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_0997","image_path":"images/combination_0997.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_0997_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_0997_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_0997_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_0997_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0997_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":997,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[560,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_0998","image_path":"images/combination_0998.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_0998_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_0998_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_0998_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_0998_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0998_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":998,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_0999","image_path":"images/combination_0999.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_0999_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_0999_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_0999_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_0999_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":999,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[599,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1000","image_path":"images/combination_1000.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1000_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1000_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1000_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":"combination_1000_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1000_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1000,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[600,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1001","image_path":"images/combination_1001.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1001_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1001_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1001_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1001_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1001_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1001,"target_cell_count":7,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[583,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1002","image_path":"images/combination_1002.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1002_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1002_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1002_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":"combination_1002_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1002_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1002,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[581,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1003","image_path":"images/combination_1003.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1003_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1003_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_1003_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1003_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1003,"target_cell_count":8,"target_cells":[[0,3],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1004","image_path":"images/combination_1004.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1004_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1004_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1004_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1004_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1004_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1004,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1005","image_path":"images/combination_1005.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1005_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1005_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1005_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":"combination_1005_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1005_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1005,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[572,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1006","image_path":"images/combination_1006.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1006_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1006_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1006_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":"combination_1006_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1006_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1006,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[552,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1007","image_path":"images/combination_1007.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1007_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1007_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1007_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":"combination_1007_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1007_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1007,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[583,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1008","image_path":"images/combination_1008.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1008_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1008_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1008_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":"combination_1008_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1008_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1008,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4],[3,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[561,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1009","image_path":"images/combination_1009.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1009_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1009_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1009_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1009_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1009,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_1010","image_path":"images/combination_1010.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1010_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1010_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1010_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1010_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1010_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1010,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[573,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1011","image_path":"images/combination_1011.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1011_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1011_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1011_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1011_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1011_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1011,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1012","image_path":"images/combination_1012.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1012_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1012_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1012_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1012_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1012_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1012,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[581,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1013","image_path":"images/combination_1013.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1013_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1013_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1013_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1013_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1013_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1013,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[582,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1014","image_path":"images/combination_1014.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1014_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1014_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1014_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1014_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1014_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1014,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1015","image_path":"images/combination_1015.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1015_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1015_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1015_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1015_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1015_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1015,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9}],"canvas_size":[573,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1016","image_path":"images/combination_1016.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1016_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1016_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1016_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":"combination_1016_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1016_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1016,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1017","image_path":"images/combination_1017.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1017_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1017_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1017_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1017_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1017_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1017,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[575,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1018","image_path":"images/combination_1018.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1018_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1018_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1018_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1018_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1018_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1018,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,4],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[552,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1019","image_path":"images/combination_1019.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1019_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1019_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1019_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":"combination_1019_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1019_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1019,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[557,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1020","image_path":"images/combination_1020.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1020_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1020_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1020_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1020_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1020_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1020,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[583,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1021","image_path":"images/combination_1021.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1021_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1021_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1021_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":"combination_1021_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1021_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1021,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[558,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1022","image_path":"images/combination_1022.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1022_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1022_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1022_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":"combination_1022_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1022_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1022,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[581,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1023","image_path":"images/combination_1023.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1023_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1023_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1023_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1023_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1023_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1023,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":9}],"canvas_size":[551,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1024","image_path":"images/combination_1024.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1024_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1024_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1024_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":"combination_1024_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1024_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1024,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[563,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1025","image_path":"images/combination_1025.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1025_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1025_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1025_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":"combination_1025_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1025_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1025,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1026","image_path":"images/combination_1026.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1026_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1026_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1026_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1026_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1026_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1026,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[551,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1027","image_path":"images/combination_1027.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1027_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1027_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1027_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":"combination_1027_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1027_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1027,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1],[4,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[579,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1028","image_path":"images/combination_1028.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1028_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1028_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1028_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1028_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1028_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1028,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]],[[0,0]]],"total_cell_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],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[588,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1029","image_path":"images/combination_1029.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1029_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1029_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1029_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1029_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1029_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1029,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":10}],"canvas_size":[553,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1030","image_path":"images/combination_1030.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1030_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1030_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1030_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1030_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1030_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1030,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[2,5],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[594,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1031","image_path":"images/combination_1031.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1031_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1031_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1031_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1031_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1031_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1031,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[574,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1032","image_path":"images/combination_1032.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1032_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1032_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1032_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1032_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1032_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1032,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[591,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1033","image_path":"images/combination_1033.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1033_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1033_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_1033_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":"combination_1033_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1033_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1033,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[552,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1034","image_path":"images/combination_1034.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1034_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1034_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1034_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1034_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1034_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1034,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_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]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9}],"canvas_size":[598,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1035","image_path":"images/combination_1035.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1035_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1035_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1035_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":"combination_1035_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1035_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1035,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[576,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1036","image_path":"images/combination_1036.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1036_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1036_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1036_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":"combination_1036_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1036_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1036,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[555,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1037","image_path":"images/combination_1037.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1037_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1037_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1037_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1037_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1037_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1037,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,4]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1038","image_path":"images/combination_1038.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1038_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1038_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1038_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":"combination_1038_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1038_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1038,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1039","image_path":"images/combination_1039.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1039_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1039_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1039_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":"combination_1039_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1039_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1039,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,0]]}
{"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],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[569,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1040","image_path":"images/combination_1040.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1040_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1040_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1040_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1040_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1040_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1040,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[578,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1041","image_path":"images/combination_1041.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1041_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1041_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1041_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":"combination_1041_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1041_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1041,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[565,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1042","image_path":"images/combination_1042.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1042_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1042_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1042_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":"combination_1042_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1042_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1042,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[587,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1043","image_path":"images/combination_1043.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1043_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1043_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1043_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1043_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1043_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1043,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[564,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1044","image_path":"images/combination_1044.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1044_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1044_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1044_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":"combination_1044_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1044_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1044,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[593,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1045","image_path":"images/combination_1045.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1045_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1045_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1045_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":"combination_1045_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1045_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1045,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9}],"canvas_size":[579,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1046","image_path":"images/combination_1046.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1046_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1046_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1046_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":"combination_1046_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1046_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1046,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[555,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1047","image_path":"images/combination_1047.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1047_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1047_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1047_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1047_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1047_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1047,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1048","image_path":"images/combination_1048.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1048_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1048_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_1048_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1048_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1048,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[593,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1049","image_path":"images/combination_1049.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1049_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1049_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1049_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1049_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1049_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1049,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[570,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1050","image_path":"images/combination_1050.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1050_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1050_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1050_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1050_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1050_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1050,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1051","image_path":"images/combination_1051.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1051_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1051_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1051_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1051_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1051_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1051,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":6}],"canvas_size":[559,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1052","image_path":"images/combination_1052.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1052_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1052_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1052_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1052_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1052_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1052,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[598,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1053","image_path":"images/combination_1053.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1053_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1053_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1053_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1053_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1053_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1053,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[557,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1054","image_path":"images/combination_1054.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1054_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1054_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1054_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":"combination_1054_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1054_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1054,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[555,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1055","image_path":"images/combination_1055.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1055_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1055_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1055_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1055_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1055_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1055,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[557,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1056","image_path":"images/combination_1056.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1056_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1056_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1056_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":"combination_1056_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1056_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1056,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[585,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1057","image_path":"images/combination_1057.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1057_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1057_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1057_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1057_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1057_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1057,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[569,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_1058","image_path":"images/combination_1058.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1058_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1058_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1058_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1058_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1058_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1058,"target_cell_count":7,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":10}],"canvas_size":[552,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1059","image_path":"images/combination_1059.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1059_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1059_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1059_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1059_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1059_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1059,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1060","image_path":"images/combination_1060.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1060_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1060_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1060_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":"combination_1060_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1060_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1060,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1061","image_path":"images/combination_1061.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1061_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1061_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1061_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":"combination_1061_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1061_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1061,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[557,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1062","image_path":"images/combination_1062.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1062_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1062_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1062_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":"combination_1062_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1062_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1062,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1063","image_path":"images/combination_1063.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1063_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1063_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1063_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1063_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1063_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1063,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1064","image_path":"images/combination_1064.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1064_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1064_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1064_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":"combination_1064_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1064_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1064,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[594,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1065","image_path":"images/combination_1065.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1065_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1065_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1065_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1065_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1065_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1065,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1066","image_path":"images/combination_1066.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1066_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1066_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1066_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1066_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1066_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1066,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[550,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1067","image_path":"images/combination_1067.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1067_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1067_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1067_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":"combination_1067_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1067_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1067,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[576,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1068","image_path":"images/combination_1068.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1068_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1068_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1068_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":"combination_1068_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1068_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1068,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1069","image_path":"images/combination_1069.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1069_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1069_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1069_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":"combination_1069_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1069_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1069,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[572,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1070","image_path":"images/combination_1070.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1070_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1070_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1070_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1070_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1070_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1070,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[557,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1071","image_path":"images/combination_1071.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1071_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1071_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1071_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1071_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1071_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1071,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1072","image_path":"images/combination_1072.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1072_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1072_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1072_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1072_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1072_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1072,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[570,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1073","image_path":"images/combination_1073.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1073_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1073_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1073_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1073_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1073_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1073,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[590,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1074","image_path":"images/combination_1074.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1074_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1074_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1074_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":"combination_1074_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1074_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1074,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[577,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1075","image_path":"images/combination_1075.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1075_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1075_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1075_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":"combination_1075_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1075_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1075,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[572,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1076","image_path":"images/combination_1076.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1076_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1076_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1076_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1076_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1076_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1076,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1077","image_path":"images/combination_1077.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1077_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1077_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1077_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1077_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1077_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1077,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1078","image_path":"images/combination_1078.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1078_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1078_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1078_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":"combination_1078_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1078_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1078,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1079","image_path":"images/combination_1079.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1079_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1079_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1079_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1079_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1079_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1079,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,4]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]],"total_cell_count":10}],"canvas_size":[600,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1080","image_path":"images/combination_1080.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1080_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1080_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1080_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":"combination_1080_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1080_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1080,"target_cell_count":10,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[580,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1081","image_path":"images/combination_1081.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1081_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1081_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1081_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":"combination_1081_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1081_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1081,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]]],"total_cell_count":10}],"canvas_size":[562,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1082","image_path":"images/combination_1082.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1082_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1082_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_1082_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":"combination_1082_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1082_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1082,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[563,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1083","image_path":"images/combination_1083.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1083_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1083_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1083_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1083_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1083,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[591,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1084","image_path":"images/combination_1084.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1084_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1084_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1084_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":"combination_1084_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1084_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1084,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[591,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1085","image_path":"images/combination_1085.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1085_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1085_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1085_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1085_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1085_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1085,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1],[4,2],[5,1],[5,2],[6,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[587,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1086","image_path":"images/combination_1086.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1086_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1086_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1086_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":"combination_1086_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1086_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1086,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[562,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1087","image_path":"images/combination_1087.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1087_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1087_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1087_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1087_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1087_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1087,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_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],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[584,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1088","image_path":"images/combination_1088.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1088_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1088_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1088_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1088_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1088_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1088,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[570,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1089","image_path":"images/combination_1089.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1089_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1089_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_1089_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1089_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1089,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_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],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1090","image_path":"images/combination_1090.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1090_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1090_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_1090_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1090_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1090,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1091","image_path":"images/combination_1091.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1091_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1091_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1091_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":"combination_1091_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1091_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1091,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[588,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1092","image_path":"images/combination_1092.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1092_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1092_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_1092_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":"combination_1092_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1092_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1092,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,4],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[571,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1093","image_path":"images/combination_1093.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1093_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1093_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_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":"combination_1093_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1093_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1093,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1094","image_path":"images/combination_1094.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1094_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1094_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1094_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1094_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1094,"target_cell_count":10,"target_cells":[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[563,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1095","image_path":"images/combination_1095.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1095_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1095_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1095_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":"combination_1095_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1095_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1095,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[590,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1096","image_path":"images/combination_1096.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1096_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1096_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1096_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1096_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1096_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1096,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5}],"canvas_size":[583,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1097","image_path":"images/combination_1097.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1097_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1097_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1097_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1097_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1097_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1097,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[561,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1098","image_path":"images/combination_1098.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1098_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1098_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1098_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1098_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1098_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1098,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":6}],"canvas_size":[575,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1099","image_path":"images/combination_1099.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1099_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1099_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1099_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":"combination_1099_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1099_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1099,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1100","image_path":"images/combination_1100.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1100_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1100_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1100_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1100_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1100,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[572,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1101","image_path":"images/combination_1101.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1101_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1101_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1101_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":"combination_1101_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1101_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1101,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1102","image_path":"images/combination_1102.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1102_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1102_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1102_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1102_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1102_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1102,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[575,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1103","image_path":"images/combination_1103.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1103_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1103_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1103_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1103_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1103_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1103,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[566,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1104","image_path":"images/combination_1104.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1104_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1104_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1104_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":"combination_1104_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1104_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1104,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1105","image_path":"images/combination_1105.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1105_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1105_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1105_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":"combination_1105_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1105_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1105,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"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],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[579,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1106","image_path":"images/combination_1106.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1106_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1106_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1106_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1106_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1106_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1106,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1107","image_path":"images/combination_1107.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1107_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1107_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1107_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":"combination_1107_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1107_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1107,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[565,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1108","image_path":"images/combination_1108.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1108_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1108_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1108_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1108_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1108_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1108,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1109","image_path":"images/combination_1109.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1109_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1109_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1109_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1109_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1109_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1109,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[580,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1110","image_path":"images/combination_1110.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1110_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1110_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1110_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1110_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1110_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1110,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7}],"canvas_size":[563,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1111","image_path":"images/combination_1111.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1111_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1111_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1111_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":"combination_1111_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1111_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1111,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[568,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1112","image_path":"images/combination_1112.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1112_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1112_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1112_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":"combination_1112_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1112_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1112,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[551,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1113","image_path":"images/combination_1113.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1113_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1113_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1113_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1113_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1113_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1113,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1114","image_path":"images/combination_1114.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1114_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1114_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1114_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":"combination_1114_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1114_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1114,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4],[1,5],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[567,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1115","image_path":"images/combination_1115.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1115_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1115_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1115_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1115_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1115_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1115,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1116","image_path":"images/combination_1116.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1116_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1116_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1116_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":"combination_1116_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1116_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1116,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1117","image_path":"images/combination_1117.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1117_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1117_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1117_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":"combination_1117_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1117_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1117,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":9}],"canvas_size":[564,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1118","image_path":"images/combination_1118.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1118_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1118_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1118_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1118_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1118_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1118,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[553,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1119","image_path":"images/combination_1119.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1119_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1119_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1119_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1119_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1119_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1119,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[588,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1120","image_path":"images/combination_1120.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1120_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1120_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1120_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":"combination_1120_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1120_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1120,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1121","image_path":"images/combination_1121.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1121_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1121_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1121_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1121_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1121_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1121,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[579,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1122","image_path":"images/combination_1122.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1122_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1122_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1122_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":"combination_1122_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1122_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1122,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[567,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1123","image_path":"images/combination_1123.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1123_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1123_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1123_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1123_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1123_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1123,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10}],"canvas_size":[552,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1124","image_path":"images/combination_1124.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1124_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1124_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1124_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1124_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1124_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1124,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,3],[1,4],[1,5],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1125","image_path":"images/combination_1125.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1125_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1125_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_1125_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":"combination_1125_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1125_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1125,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1126","image_path":"images/combination_1126.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1126_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1126_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1126_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":"combination_1126_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1126_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1126,"target_cell_count":7,"target_cells":[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[581,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1127","image_path":"images/combination_1127.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1127_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1127_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1127_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":"combination_1127_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1127_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1127,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1128","image_path":"images/combination_1128.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1128_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1128_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1128_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1128_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1128_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1128,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[596,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1129","image_path":"images/combination_1129.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1129_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1129_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_1129_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1129_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1129,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1130","image_path":"images/combination_1130.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1130_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1130_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1130_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1130_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1130_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1130,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[550,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1131","image_path":"images/combination_1131.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1131_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1131_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1131_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1131_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1131_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1131,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[584,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1132","image_path":"images/combination_1132.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1132_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1132_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1132_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1132_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1132_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1132,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":8}],"canvas_size":[576,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1133","image_path":"images/combination_1133.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1133_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1133_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1133_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":"combination_1133_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1133_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1133,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[552,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1134","image_path":"images/combination_1134.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1134_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1134_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1134_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1134_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1134_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1134,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[584,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1135","image_path":"images/combination_1135.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1135_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1135_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1135_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":"combination_1135_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1135_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1135,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1136","image_path":"images/combination_1136.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1136_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1136_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1136_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1136_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1136,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1137","image_path":"images/combination_1137.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1137_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1137_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1137_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":"combination_1137_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1137_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1137,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,4]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[568,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1138","image_path":"images/combination_1138.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1138_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1138_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1138_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":"combination_1138_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1138_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1138,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[557,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1139","image_path":"images/combination_1139.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1139_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1139_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1139_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1139_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1139,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[573,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1140","image_path":"images/combination_1140.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1140_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1140_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1140_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1140_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1140_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1140,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[575,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1141","image_path":"images/combination_1141.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1141_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1141_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1141_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1141_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1141_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1141,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1142","image_path":"images/combination_1142.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1142_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1142_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1142_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1142_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1142_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1142,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[592,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1143","image_path":"images/combination_1143.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1143_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1143_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1143_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":"combination_1143_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1143_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1143,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[582,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1144","image_path":"images/combination_1144.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1144_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1144_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1144_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":"combination_1144_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1144_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1144,"target_cell_count":9,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1145","image_path":"images/combination_1145.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1145_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1145_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1145_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1145_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1145_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1145,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[595,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1146","image_path":"images/combination_1146.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1146_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1146_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1146_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":"combination_1146_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1146_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1146,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[559,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1147","image_path":"images/combination_1147.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1147_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1147_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_1147_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":"combination_1147_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1147_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1147,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[578,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1148","image_path":"images/combination_1148.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1148_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1148_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_1148_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1148_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1148,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[586,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1149","image_path":"images/combination_1149.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1149_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1149_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1149_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1149_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1149_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1149,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,1],[2,2],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1150","image_path":"images/combination_1150.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1150_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1150_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1150_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1150_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1150_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1150,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[558,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1151","image_path":"images/combination_1151.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1151_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1151_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1151_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":"combination_1151_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1151_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1151,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[586,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1152","image_path":"images/combination_1152.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1152_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1152_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1152_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":"combination_1152_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1152_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1152,"target_cell_count":10,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,2],[4,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[554,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1153","image_path":"images/combination_1153.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1153_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1153_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1153_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1153_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1153_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1153,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[584,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1154","image_path":"images/combination_1154.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1154_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1154_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1154_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":"combination_1154_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1154_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1154,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":10}],"canvas_size":[562,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1155","image_path":"images/combination_1155.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1155_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1155_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1155_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1155_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1155_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1155,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9}],"canvas_size":[588,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1156","image_path":"images/combination_1156.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1156_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1156_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1156_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":"combination_1156_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1156_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1156,"target_cell_count":9,"target_cells":[[0,4],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]],"total_cell_count":8}],"canvas_size":[586,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1157","image_path":"images/combination_1157.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1157_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1157_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1157_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":"combination_1157_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1157_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1157,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1158","image_path":"images/combination_1158.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1158_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1158_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1158_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":"combination_1158_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1158_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1158,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1159","image_path":"images/combination_1159.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1159_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1159_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1159_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":"combination_1159_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1159_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1159,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[578,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1160","image_path":"images/combination_1160.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1160_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1160_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1160_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":"combination_1160_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1160_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1160,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"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]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[585,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1161","image_path":"images/combination_1161.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1161_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1161_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1161_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1161_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1161_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1161,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1162","image_path":"images/combination_1162.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1162_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1162_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1162_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":"combination_1162_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1162_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1162,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1163","image_path":"images/combination_1163.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1163_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1163_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1163_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":"combination_1163_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1163_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1163,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1164","image_path":"images/combination_1164.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1164_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1164_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1164_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":"combination_1164_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1164_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1164,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[559,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1165","image_path":"images/combination_1165.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1165_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1165_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1165_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":"combination_1165_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1165_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1165,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1166","image_path":"images/combination_1166.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1166_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1166_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1166_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1166_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1166_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1166,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9}],"canvas_size":[596,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1167","image_path":"images/combination_1167.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1167_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1167_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1167_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1167_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1167_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1167,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,4],[1,1],[1,2],[1,3],[1,4],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[588,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1168","image_path":"images/combination_1168.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1168_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1168_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1168_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1168_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1168_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1168,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[551,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1169","image_path":"images/combination_1169.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1169_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1169_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1169_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1169_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1169_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1169,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1170","image_path":"images/combination_1170.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1170_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1170_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1170_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1170_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1170_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1170,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[596,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1171","image_path":"images/combination_1171.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1171_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1171_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1171_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":"combination_1171_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1171_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1171,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[585,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1172","image_path":"images/combination_1172.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1172_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1172_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1172_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":"combination_1172_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1172_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1172,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2],[4,3],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1173","image_path":"images/combination_1173.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1173_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1173_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1173_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":"combination_1173_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1173_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1173,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[564,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1174","image_path":"images/combination_1174.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1174_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1174_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_1174_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1174_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1174,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[577,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1175","image_path":"images/combination_1175.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1175_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1175_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1175_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":"combination_1175_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1175_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1175,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[600,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1176","image_path":"images/combination_1176.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1176_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1176_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1176_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":"combination_1176_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1176_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1176,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[575,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1177","image_path":"images/combination_1177.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1177_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1177_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1177_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1177_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1177_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1177,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[588,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1178","image_path":"images/combination_1178.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1178_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1178_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1178_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1178_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1178_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1178,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6}],"canvas_size":[586,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1179","image_path":"images/combination_1179.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1179_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1179_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1179_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1179_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1179_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1179,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1180","image_path":"images/combination_1180.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1180_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1180_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1180_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1180_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1180_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1180,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[573,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1181","image_path":"images/combination_1181.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1181_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1181_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1181_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":"combination_1181_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1181_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1181,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[593,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1182","image_path":"images/combination_1182.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1182_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1182_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1182_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1182_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1182_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1182,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[573,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1183","image_path":"images/combination_1183.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1183_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1183_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1183_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":"combination_1183_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1183_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1183,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8}],"canvas_size":[582,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1184","image_path":"images/combination_1184.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1184_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1184_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1184_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1184_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1184_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1184,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[566,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1185","image_path":"images/combination_1185.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1185_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1185_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1185_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1185_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1185_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1185,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1186","image_path":"images/combination_1186.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1186_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1186_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1186_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":"combination_1186_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1186_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1186,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7}],"canvas_size":[596,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1187","image_path":"images/combination_1187.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1187_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1187_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1187_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1187_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1187,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[587,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1188","image_path":"images/combination_1188.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1188_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1188_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1188_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":"combination_1188_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1188_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1188,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,3],[2,1],[2,2],[2,3],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,1],[2,3],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,3],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[586,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1189","image_path":"images/combination_1189.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1189_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1189_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1189_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1189_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1189_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1189,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":10}],"canvas_size":[578,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1190","image_path":"images/combination_1190.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1190_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1190_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1190_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1190_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1190_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1190,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[576,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1191","image_path":"images/combination_1191.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1191_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1191_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1191_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1191_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1191_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1191,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[597,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1192","image_path":"images/combination_1192.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1192_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1192_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1192_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":"combination_1192_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1192_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1192,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[569,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1193","image_path":"images/combination_1193.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1193_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1193_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_1193_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1193_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1193,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[4,0],[4,1],[5,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0],[5,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[4,0],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[590,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1194","image_path":"images/combination_1194.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1194_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1194_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1194_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":"combination_1194_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1194_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1194,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2],[3,3],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[569,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1195","image_path":"images/combination_1195.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1195_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1195_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1195_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":"combination_1195_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1195_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1195,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1196","image_path":"images/combination_1196.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1196_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1196_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1196_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":"combination_1196_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1196_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1196,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[592,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1197","image_path":"images/combination_1197.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1197_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1197_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1197_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":"combination_1197_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1197_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1197,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1198","image_path":"images/combination_1198.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1198_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1198_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1198_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":"combination_1198_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1198_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1198,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[597,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1199","image_path":"images/combination_1199.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1199_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1199_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1199_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":"combination_1199_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1199_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1199,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[569,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1200","image_path":"images/combination_1200.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1200_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1200_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1200_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1200_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1200_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1200,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1201","image_path":"images/combination_1201.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1201_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1201_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1201_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":"combination_1201_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1201_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1201,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[569,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1202","image_path":"images/combination_1202.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1202_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1202_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1202_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":"combination_1202_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1202_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1202,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[563,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1203","image_path":"images/combination_1203.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1203_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1203_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1203_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":"combination_1203_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1203_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1203,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1204","image_path":"images/combination_1204.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1204_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1204_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1204_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":"combination_1204_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1204_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1204,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_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],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1205","image_path":"images/combination_1205.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1205_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1205_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1205_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1205_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1205_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1205,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[571,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1206","image_path":"images/combination_1206.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1206_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1206_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1206_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1206_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1206_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1206,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[595,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1207","image_path":"images/combination_1207.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1207_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1207_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1207_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":"combination_1207_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1207_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1207,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[551,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1208","image_path":"images/combination_1208.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1208_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1208_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1208_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1208_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1208_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1208,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[584,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1209","image_path":"images/combination_1209.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1209_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1209_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1209_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1209_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1209_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1209,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[1,5]]],"total_cell_count":9}],"canvas_size":[554,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1210","image_path":"images/combination_1210.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1210_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1210_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1210_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1210_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1210,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0],[5,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[5,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[568,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1211","image_path":"images/combination_1211.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1211_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1211_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1211_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":"combination_1211_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1211_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1211,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[4,2],[5,1],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[600,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1212","image_path":"images/combination_1212.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1212_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1212_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1212_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1212_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1212_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1212,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[582,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1213","image_path":"images/combination_1213.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1213_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1213_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1213_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1213_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1213_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1213,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[567,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1214","image_path":"images/combination_1214.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1214_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1214_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1214_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1214_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1214_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1214,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[578,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1215","image_path":"images/combination_1215.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1215_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1215_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1215_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":"combination_1215_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1215_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1215,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1216","image_path":"images/combination_1216.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1216_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1216_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1216_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":"combination_1216_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1216_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1216,"target_cell_count":6,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[553,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1217","image_path":"images/combination_1217.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1217_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1217_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1217_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1217_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1217_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1217,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1218","image_path":"images/combination_1218.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1218_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1218_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1218_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1218_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1218_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1218,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[583,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1219","image_path":"images/combination_1219.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1219_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1219_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1219_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":"combination_1219_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1219_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1219,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1220","image_path":"images/combination_1220.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1220_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1220_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1220_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":"combination_1220_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1220_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1220,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1221","image_path":"images/combination_1221.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1221_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1221_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1221_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1221_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1221,"target_cell_count":8,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[586,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1222","image_path":"images/combination_1222.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1222_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1222_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1222_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1222_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1222_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1222,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[597,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1223","image_path":"images/combination_1223.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1223_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1223_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1223_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1223_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1223_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1223,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1224","image_path":"images/combination_1224.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1224_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1224_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1224_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1224_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1224_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1224,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":7}],"canvas_size":[574,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1225","image_path":"images/combination_1225.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1225_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1225_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1225_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":"combination_1225_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1225_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1225,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[579,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_1226","image_path":"images/combination_1226.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1226_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1226_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1226_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1226_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1226_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1226,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1227","image_path":"images/combination_1227.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1227_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1227_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1227_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":"combination_1227_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1227_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1227,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[557,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1228","image_path":"images/combination_1228.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1228_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1228_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1228_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1228_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1228_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1228,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[558,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1229","image_path":"images/combination_1229.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1229_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1229_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1229_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":"combination_1229_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1229_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1229,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[585,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1230","image_path":"images/combination_1230.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1230_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1230_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1230_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1230_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1230_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1230,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[574,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1231","image_path":"images/combination_1231.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1231_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1231_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1231_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1231_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1231_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1231,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1232","image_path":"images/combination_1232.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1232_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1232_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1232_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1232_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1232_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1232,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[570,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1233","image_path":"images/combination_1233.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1233_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1233_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1233_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1233_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1233_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1233,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[599,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1234","image_path":"images/combination_1234.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1234_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1234_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1234_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":"combination_1234_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1234_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1234,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[594,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1235","image_path":"images/combination_1235.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1235_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1235_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1235_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":"combination_1235_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1235_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1235,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[584,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1236","image_path":"images/combination_1236.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1236_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1236_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1236_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":"combination_1236_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1236_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1236,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[559,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1237","image_path":"images/combination_1237.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1237_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1237_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_1237_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1237_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1237,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[551,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1238","image_path":"images/combination_1238.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1238_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1238_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1238_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":"combination_1238_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1238_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1238,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1239","image_path":"images/combination_1239.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1239_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1239_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1239_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":"combination_1239_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1239_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1239,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[591,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1240","image_path":"images/combination_1240.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1240_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1240_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1240_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1240_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1240_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1240,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[588,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1241","image_path":"images/combination_1241.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1241_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1241_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1241_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1241_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1241_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1241,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[555,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1242","image_path":"images/combination_1242.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1242_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1242_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1242_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":"combination_1242_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1242_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1242,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[596,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1243","image_path":"images/combination_1243.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1243_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1243_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1243_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1243_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1243_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1243,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[567,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1244","image_path":"images/combination_1244.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1244_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1244_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1244_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1244_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1244_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1244,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1245","image_path":"images/combination_1245.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1245_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1245_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1245_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":"combination_1245_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1245_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1245,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,3],[1,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1246","image_path":"images/combination_1246.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1246_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1246_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1246_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1246_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1246_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1246,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6}],"canvas_size":[599,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1247","image_path":"images/combination_1247.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1247_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1247_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1247_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":"combination_1247_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1247_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1247,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[586,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1248","image_path":"images/combination_1248.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1248_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1248_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1248_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":"combination_1248_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1248_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1248,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[582,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1249","image_path":"images/combination_1249.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1249_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1249_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1249_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1249_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1249_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1249,"target_cell_count":7,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7}],"canvas_size":[559,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1250","image_path":"images/combination_1250.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1250_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1250_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1250_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":"combination_1250_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1250_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1250,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[594,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1251","image_path":"images/combination_1251.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1251_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1251_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1251_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":"combination_1251_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1251_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1251,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[600,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1252","image_path":"images/combination_1252.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1252_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1252_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1252_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":"combination_1252_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1252_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1252,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1253","image_path":"images/combination_1253.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1253_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1253_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1253_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1253_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1253_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1253,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[577,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1254","image_path":"images/combination_1254.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1254_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1254_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1254_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1254_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1254_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1254,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6}],"canvas_size":[574,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1255","image_path":"images/combination_1255.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1255_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1255_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1255_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1255_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1255_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1255,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[585,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1256","image_path":"images/combination_1256.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1256_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1256_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1256_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":"combination_1256_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1256_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1256,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[582,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1257","image_path":"images/combination_1257.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1257_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1257_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1257_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1257_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1257_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1257,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[558,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1258","image_path":"images/combination_1258.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1258_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1258_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1258_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1258_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1258_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1258,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[574,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1259","image_path":"images/combination_1259.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1259_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1259_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1259_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1259_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1259_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1259,"target_cell_count":7,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[555,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1260","image_path":"images/combination_1260.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1260_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1260_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1260_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1260_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1260,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1261","image_path":"images/combination_1261.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1261_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1261_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1261_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1261_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1261_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1261,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1262","image_path":"images/combination_1262.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1262_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1262_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1262_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":"combination_1262_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1262_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1262,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1263","image_path":"images/combination_1263.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1263_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1263_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1263_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1263_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1263_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1263,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[557,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1264","image_path":"images/combination_1264.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1264_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1264_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1264_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1264_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1264_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1264,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1265","image_path":"images/combination_1265.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1265_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1265_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1265_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":"combination_1265_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1265_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1265,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1266","image_path":"images/combination_1266.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1266_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1266_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1266_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":"combination_1266_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1266_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1266,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[554,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1267","image_path":"images/combination_1267.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1267_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1267_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1267_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1267_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1267_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1267,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1268","image_path":"images/combination_1268.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1268_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1268_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1268_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":"combination_1268_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1268_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1268,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[597,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1269","image_path":"images/combination_1269.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1269_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1269_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1269_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":"combination_1269_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1269_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1269,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[586,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1270","image_path":"images/combination_1270.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1270_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1270_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1270_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1270_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1270_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1270,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[3,2],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":10}],"canvas_size":[572,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1271","image_path":"images/combination_1271.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1271_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1271_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1271_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":"combination_1271_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1271_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1271,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[564,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1272","image_path":"images/combination_1272.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1272_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1272_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1272_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":"combination_1272_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1272_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1272,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]],"total_cell_count":10}],"canvas_size":[592,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1273","image_path":"images/combination_1273.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1273_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1273_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1273_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1273_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1273_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1273,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1274","image_path":"images/combination_1274.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1274_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1274_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1274_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":"combination_1274_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1274_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1274,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[591,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1275","image_path":"images/combination_1275.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1275_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1275_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1275_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1275_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1275_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1275,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[565,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1276","image_path":"images/combination_1276.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1276_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1276_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1276_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":"combination_1276_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1276_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1276,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[564,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1277","image_path":"images/combination_1277.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1277_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1277_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1277_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":"combination_1277_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1277_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1277,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[553,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1278","image_path":"images/combination_1278.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1278_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1278_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1278_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":"combination_1278_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1278_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1278,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[596,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1279","image_path":"images/combination_1279.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1279_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1279_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1279_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":"combination_1279_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1279_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1279,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"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],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[597,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1280","image_path":"images/combination_1280.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1280_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1280_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1280_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1280_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1280_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1280,"target_cell_count":8,"target_cells":[[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[564,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1281","image_path":"images/combination_1281.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1281_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1281_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1281_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1281_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1281_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1281,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[553,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1282","image_path":"images/combination_1282.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1282_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1282_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1282_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1282_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1282_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1282,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[570,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1283","image_path":"images/combination_1283.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1283_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1283_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1283_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1283_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1283_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1283,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[581,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1284","image_path":"images/combination_1284.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1284_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1284_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1284_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":"combination_1284_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1284_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1284,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[566,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1285","image_path":"images/combination_1285.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1285_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1285_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1285_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1285_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1285_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1285,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[571,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1286","image_path":"images/combination_1286.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1286_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1286_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1286_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":"combination_1286_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1286_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1286,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1287","image_path":"images/combination_1287.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1287_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1287_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_1287_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1287_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1287,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1288","image_path":"images/combination_1288.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1288_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1288_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1288_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":"combination_1288_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1288_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1288,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[586,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1289","image_path":"images/combination_1289.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1289_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1289_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1289_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":"combination_1289_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1289_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1289,"target_cell_count":7,"target_cells":[[0,3],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1290","image_path":"images/combination_1290.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1290_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1290_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1290_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":"combination_1290_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1290_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1290,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[586,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1291","image_path":"images/combination_1291.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1291_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1291_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1291_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1291_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1291_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1291,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2],[4,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[4,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":10}],"canvas_size":[576,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1292","image_path":"images/combination_1292.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1292_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1292_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1292_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1292_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1292_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1292,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[1,2],[2,2],[3,2],[4,0],[4,1],[4,2],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1293","image_path":"images/combination_1293.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1293_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1293_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1293_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":"combination_1293_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1293_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1293,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[573,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_1294","image_path":"images/combination_1294.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1294_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1294_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1294_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1294_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1294_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1294,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[556,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1295","image_path":"images/combination_1295.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1295_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1295_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1295_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":"combination_1295_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1295_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1295,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1296","image_path":"images/combination_1296.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1296_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1296_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1296_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":"combination_1296_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1296_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1296,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[578,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1297","image_path":"images/combination_1297.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1297_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1297_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1297_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1297_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1297_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1297,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[562,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1298","image_path":"images/combination_1298.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1298_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1298_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1298_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1298_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1298_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1298,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[570,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1299","image_path":"images/combination_1299.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1299_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1299_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_1299_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1299_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1299,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[573,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1300","image_path":"images/combination_1300.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1300_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1300_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1300_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":"combination_1300_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1300_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1300,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[577,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1301","image_path":"images/combination_1301.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1301_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1301_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1301_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":"combination_1301_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1301_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1301,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":10}],"canvas_size":[580,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1302","image_path":"images/combination_1302.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1302_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1302_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1302_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1302_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1302_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1302,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]],"total_cell_count":10}],"canvas_size":[573,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1303","image_path":"images/combination_1303.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1303_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1303_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1303_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1303_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1303_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1303,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":10}],"canvas_size":[575,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1304","image_path":"images/combination_1304.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1304_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1304_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1304_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1304_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1304_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1304,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[560,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1305","image_path":"images/combination_1305.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1305_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1305_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1305_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1305_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1305_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1305,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[600,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1306","image_path":"images/combination_1306.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1306_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1306_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1306_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1306_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1306_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1306,"target_cell_count":9,"target_cells":[[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":10}],"canvas_size":[586,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1307","image_path":"images/combination_1307.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1307_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1307_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1307_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1307_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1307_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1307,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[581,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1308","image_path":"images/combination_1308.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1308_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1308_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1308_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1308_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1308_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1308,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[581,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1309","image_path":"images/combination_1309.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1309_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1309_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1309_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1309_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1309_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1309,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[565,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1310","image_path":"images/combination_1310.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1310_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1310_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1310_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1310_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1310_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1310,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[559,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1311","image_path":"images/combination_1311.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1311_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1311_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1311_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":"combination_1311_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1311_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1311,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[585,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1312","image_path":"images/combination_1312.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1312_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1312_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1312_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1312_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1312_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1312,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1313","image_path":"images/combination_1313.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1313_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1313_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1313_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":"combination_1313_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1313_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1313,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[575,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1314","image_path":"images/combination_1314.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1314_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1314_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1314_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1314_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1314_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1314,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1315","image_path":"images/combination_1315.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1315_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1315_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1315_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1315_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1315_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1315,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[563,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1316","image_path":"images/combination_1316.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1316_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1316_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1316_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1316_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1316_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1316,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[589,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1317","image_path":"images/combination_1317.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1317_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1317_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1317_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1317_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1317_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1317,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[596,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1318","image_path":"images/combination_1318.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1318_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1318_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1318_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":"combination_1318_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1318_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1318,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[575,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1319","image_path":"images/combination_1319.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1319_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1319_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1319_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1319_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1319_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1319,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[559,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1320","image_path":"images/combination_1320.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1320_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1320_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1320_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1320_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1320_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1320,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1321","image_path":"images/combination_1321.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1321_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1321_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1321_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1321_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1321_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1321,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[576,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1322","image_path":"images/combination_1322.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1322_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1322_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1322_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":"combination_1322_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1322_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1322,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[580,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1323","image_path":"images/combination_1323.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1323_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1323_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1323_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1323_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1323_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1323,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[580,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1324","image_path":"images/combination_1324.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1324_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1324_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1324_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":"combination_1324_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1324_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1324,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[598,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1325","image_path":"images/combination_1325.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1325_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1325_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1325_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":"combination_1325_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1325_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1325,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[581,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1326","image_path":"images/combination_1326.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1326_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1326_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1326_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":"combination_1326_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1326_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1326,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[564,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1327","image_path":"images/combination_1327.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1327_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1327_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1327_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":"combination_1327_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1327_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1327,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[3,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[559,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1328","image_path":"images/combination_1328.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1328_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1328_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1328_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":"combination_1328_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1328_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1328,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[575,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1329","image_path":"images/combination_1329.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1329_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1329_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1329_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1329_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1329_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1329,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[572,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1330","image_path":"images/combination_1330.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1330_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1330_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1330_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1330_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1330_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1330,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8}],"canvas_size":[586,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1331","image_path":"images/combination_1331.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1331_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1331_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1331_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1331_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1331_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1331,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":7}],"canvas_size":[553,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1332","image_path":"images/combination_1332.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1332_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1332_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1332_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":"combination_1332_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1332_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1332,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1333","image_path":"images/combination_1333.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1333_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1333_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1333_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1333_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1333_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1333,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1334","image_path":"images/combination_1334.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1334_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1334_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1334_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":"combination_1334_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1334_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1334,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1335","image_path":"images/combination_1335.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1335_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1335_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1335_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1335_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1335_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1335,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,0],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[582,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1336","image_path":"images/combination_1336.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1336_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1336_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1336_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":"combination_1336_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1336_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1336,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[589,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1337","image_path":"images/combination_1337.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1337_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1337_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1337_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1337_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1337_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1337,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[599,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1338","image_path":"images/combination_1338.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1338_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1338_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1338_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1338_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1338_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1338,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[590,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1339","image_path":"images/combination_1339.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1339_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1339_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1339_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1339_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1339_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1339,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1340","image_path":"images/combination_1340.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1340_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1340_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1340_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1340_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1340_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1340,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[578,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1341","image_path":"images/combination_1341.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1341_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1341_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1341_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1341_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1341_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1341,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,3]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[554,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1342","image_path":"images/combination_1342.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1342_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1342_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1342_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1342_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1342_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1342,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1343","image_path":"images/combination_1343.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1343_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1343_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1343_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":"combination_1343_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1343_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1343,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[576,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1344","image_path":"images/combination_1344.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1344_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1344_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1344_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1344_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1344_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1344,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1345","image_path":"images/combination_1345.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1345_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1345_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1345_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1345_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1345_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1345,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1346","image_path":"images/combination_1346.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1346_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1346_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1346_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1346_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1346_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1346,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[581,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1347","image_path":"images/combination_1347.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1347_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1347_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1347_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":"combination_1347_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1347_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1347,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7}],"canvas_size":[574,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1348","image_path":"images/combination_1348.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1348_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1348_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1348_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":"combination_1348_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1348_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1348,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]],"total_cell_count":10}],"canvas_size":[550,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1349","image_path":"images/combination_1349.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1349_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1349_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1349_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1349_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1349_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1349,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[581,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1350","image_path":"images/combination_1350.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1350_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1350_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1350_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1350_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1350_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1350,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[560,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1351","image_path":"images/combination_1351.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1351_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1351_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1351_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1351_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1351_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1351,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1352","image_path":"images/combination_1352.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1352_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1352_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1352_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":"combination_1352_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1352_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1352,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_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],[1,2],[1,3],[2,0],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1353","image_path":"images/combination_1353.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1353_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1353_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1353_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1353_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1353_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1353,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1354","image_path":"images/combination_1354.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1354_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1354_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1354_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1354_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1354_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1354,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1355","image_path":"images/combination_1355.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1355_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1355_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1355_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":"combination_1355_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1355_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1355,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1356","image_path":"images/combination_1356.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1356_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1356_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1356_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1356_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1356_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1356,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[586,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1357","image_path":"images/combination_1357.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1357_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1357_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1357_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1357_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1357_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1357,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[550,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1358","image_path":"images/combination_1358.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1358_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1358_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1358_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1358_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1358_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1358,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[580,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1359","image_path":"images/combination_1359.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1359_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1359_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1359_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1359_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1359_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1359,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9}],"canvas_size":[590,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1360","image_path":"images/combination_1360.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1360_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1360_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1360_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1360_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1360_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1360,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1361","image_path":"images/combination_1361.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1361_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1361_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1361_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":"combination_1361_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1361_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1361,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1362","image_path":"images/combination_1362.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1362_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1362_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1362_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":"combination_1362_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1362_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1362,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[562,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1363","image_path":"images/combination_1363.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1363_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1363_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1363_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":"combination_1363_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1363_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1363,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[598,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1364","image_path":"images/combination_1364.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1364_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1364_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1364_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":"combination_1364_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1364_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1364,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[581,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1365","image_path":"images/combination_1365.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1365_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1365_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1365_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1365_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1365_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1365,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1366","image_path":"images/combination_1366.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1366_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1366_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1366_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":"combination_1366_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1366_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1366,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[576,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1367","image_path":"images/combination_1367.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1367_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1367_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1367_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":"combination_1367_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1367_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1367,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[563,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1368","image_path":"images/combination_1368.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1368_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1368_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1368_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1368_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1368_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1368,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[587,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1369","image_path":"images/combination_1369.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1369_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1369_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1369_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":"combination_1369_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1369_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1369,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[591,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1370","image_path":"images/combination_1370.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1370_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1370_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1370_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1370_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1370_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1370,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1371","image_path":"images/combination_1371.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1371_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1371_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1371_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":"combination_1371_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1371_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1371,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[595,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1372","image_path":"images/combination_1372.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1372_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1372_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1372_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1372_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1372_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1372,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[552,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1373","image_path":"images/combination_1373.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1373_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1373_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1373_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":"combination_1373_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1373_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1373,"target_cell_count":7,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[550,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1374","image_path":"images/combination_1374.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1374_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1374_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1374_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1374_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1374_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1374,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1375","image_path":"images/combination_1375.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1375_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1375_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1375_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":"combination_1375_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1375_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1375,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[579,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1376","image_path":"images/combination_1376.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1376_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1376_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1376_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":"combination_1376_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1376_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1376,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[559,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1377","image_path":"images/combination_1377.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1377_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1377_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1377_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1377_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1377_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1377,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[550,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1378","image_path":"images/combination_1378.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1378_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1378_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1378_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":"combination_1378_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1378_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1378,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[595,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1379","image_path":"images/combination_1379.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1379_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1379_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1379_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1379_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1379_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1379,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[591,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1380","image_path":"images/combination_1380.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1380_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1380_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1380_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1380_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1380_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1380,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[586,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1381","image_path":"images/combination_1381.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1381_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1381_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1381_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1381_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1381_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1381,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[592,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1382","image_path":"images/combination_1382.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1382_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1382_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1382_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1382_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1382_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1382,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8}],"canvas_size":[557,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1383","image_path":"images/combination_1383.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1383_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1383_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1383_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":"combination_1383_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1383_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1383,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1384","image_path":"images/combination_1384.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1384_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1384_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1384_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":"combination_1384_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1384_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1384,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7}],"canvas_size":[559,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1385","image_path":"images/combination_1385.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1385_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1385_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1385_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":"combination_1385_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1385_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1385,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[587,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1386","image_path":"images/combination_1386.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1386_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1386_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1386_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":"combination_1386_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1386_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1386,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,3]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[554,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1387","image_path":"images/combination_1387.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1387_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1387_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1387_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":"combination_1387_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1387_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1387,"target_cell_count":10,"target_cells":[[0,3],[0,4],[0,5],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1388","image_path":"images/combination_1388.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1388_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1388_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1388_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1388_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1388_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1388,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[553,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1389","image_path":"images/combination_1389.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1389_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1389_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1389_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1389_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1389_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1389,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[555,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1390","image_path":"images/combination_1390.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1390_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1390_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1390_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1390_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1390_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1390,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1391","image_path":"images/combination_1391.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1391_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1391_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1391_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1391_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1391_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1391,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1392","image_path":"images/combination_1392.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1392_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1392_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1392_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":"combination_1392_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1392_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1392,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[574,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1393","image_path":"images/combination_1393.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1393_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1393_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1393_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":"combination_1393_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1393_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1393,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,2],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[575,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1394","image_path":"images/combination_1394.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1394_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1394_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1394_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1394_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1394,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0],[5,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1395","image_path":"images/combination_1395.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1395_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1395_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1395_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1395_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1395_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1395,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1396","image_path":"images/combination_1396.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1396_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1396_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1396_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1396_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1396_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1396,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_1397","image_path":"images/combination_1397.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1397_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1397_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1397_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":"combination_1397_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1397_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1397,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1398","image_path":"images/combination_1398.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1398_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1398_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1398_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":"combination_1398_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1398_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1398,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[583,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1399","image_path":"images/combination_1399.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1399_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1399_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1399_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1399_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1399_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1399,"target_cell_count":9,"target_cells":[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[560,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1400","image_path":"images/combination_1400.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1400_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1400_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1400_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":"combination_1400_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1400_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1400,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1401","image_path":"images/combination_1401.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1401_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1401_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1401_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":"combination_1401_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1401_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1401,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[589,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1402","image_path":"images/combination_1402.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1402_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1402_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1402_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":"combination_1402_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1402_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1402,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[570,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1403","image_path":"images/combination_1403.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1403_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1403_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1403_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":"combination_1403_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1403_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1403,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[599,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1404","image_path":"images/combination_1404.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1404_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1404_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1404_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":"combination_1404_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1404_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1404,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[577,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1405","image_path":"images/combination_1405.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1405_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1405_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1405_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":"combination_1405_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1405_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1405,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[561,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1406","image_path":"images/combination_1406.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1406_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1406_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1406_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1406_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1406_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1406,"target_cell_count":9,"target_cells":[[0,4],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":8}],"canvas_size":[555,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1407","image_path":"images/combination_1407.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1407_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1407_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1407_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1407_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1407_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1407,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[581,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1408","image_path":"images/combination_1408.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1408_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1408_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_1408_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1408_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1408,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1409","image_path":"images/combination_1409.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1409_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1409_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1409_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":"combination_1409_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1409_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1409,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[568,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1410","image_path":"images/combination_1410.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1410_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1410_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1410_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1410_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1410_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1410,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[598,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1411","image_path":"images/combination_1411.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1411_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1411_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1411_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1411_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1411_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1411,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1412","image_path":"images/combination_1412.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1412_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1412_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1412_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1412_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1412_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1412,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[579,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1413","image_path":"images/combination_1413.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1413_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1413_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1413_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1413_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1413_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1413,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[558,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1414","image_path":"images/combination_1414.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1414_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1414_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1414_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1414_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1414,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":9}],"canvas_size":[584,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1415","image_path":"images/combination_1415.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1415_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1415_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1415_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1415_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1415_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1415,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1416","image_path":"images/combination_1416.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1416_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1416_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1416_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1416_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1416_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1416,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[570,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1417","image_path":"images/combination_1417.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1417_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1417_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1417_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":"combination_1417_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1417_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1417,"target_cell_count":6,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":8}],"canvas_size":[599,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1418","image_path":"images/combination_1418.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1418_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1418_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1418_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1418_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1418_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1418,"target_cell_count":8,"target_cells":[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":5}],"canvas_size":[586,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1419","image_path":"images/combination_1419.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1419_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1419_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1419_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":"combination_1419_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1419_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1419,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[596,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1420","image_path":"images/combination_1420.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1420_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1420_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1420_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1420_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1420_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1420,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1421","image_path":"images/combination_1421.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1421_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1421_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1421_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1421_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1421_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1421,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":9}],"canvas_size":[563,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1422","image_path":"images/combination_1422.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1422_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1422_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1422_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":"combination_1422_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1422_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1422,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1423","image_path":"images/combination_1423.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1423_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1423_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1423_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1423_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1423_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1423,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,4],[1,5],[1,6]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,4],[0,5],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,4],[0,5],[0,6],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1424","image_path":"images/combination_1424.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1424_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1424_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1424_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":"combination_1424_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1424_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1424,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,3],[0,4],[0,5],[0,6],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":9}],"canvas_size":[570,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1425","image_path":"images/combination_1425.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1425_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1425_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1425_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":"combination_1425_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1425_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1425,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[555,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1426","image_path":"images/combination_1426.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1426_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1426_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1426_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1426_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1426_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1426,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[598,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1427","image_path":"images/combination_1427.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1427_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1427_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1427_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1427_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1427_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1427,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[583,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1428","image_path":"images/combination_1428.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1428_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1428_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1428_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":"combination_1428_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1428_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1428,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[557,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1429","image_path":"images/combination_1429.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1429_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1429_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1429_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1429_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1429_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1429,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":9}],"canvas_size":[568,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1430","image_path":"images/combination_1430.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1430_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1430_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1430_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1430_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1430_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1430,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[583,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1431","image_path":"images/combination_1431.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1431_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1431_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1431_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1431_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1431_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1431,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1432","image_path":"images/combination_1432.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1432_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1432_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1432_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":"combination_1432_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1432_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1432,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[596,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1433","image_path":"images/combination_1433.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1433_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1433_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1433_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":"combination_1433_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1433_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1433,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[550,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1434","image_path":"images/combination_1434.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1434_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1434_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1434_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":"combination_1434_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1434_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1434,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_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],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[568,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1435","image_path":"images/combination_1435.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1435_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1435_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1435_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1435_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1435_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1435,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3],[2,4],[3,2],[3,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[600,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1436","image_path":"images/combination_1436.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1436_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1436_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1436_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1436_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1436_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1436,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,4],[2,5]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10}],"canvas_size":[563,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1437","image_path":"images/combination_1437.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1437_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1437_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1437_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":"combination_1437_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1437_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1437,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[2,5],[2,6]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,2],[3,1],[3,2],[4,0],[4,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,2],[4,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[578,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1438","image_path":"images/combination_1438.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1438_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1438_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1438_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1438_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1438_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1438,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,2],[2,3],[3,1],[3,2],[3,3],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[582,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1439","image_path":"images/combination_1439.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1439_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1439_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1439_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":"combination_1439_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1439_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1439,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[565,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1440","image_path":"images/combination_1440.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1440_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1440_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1440_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":"combination_1440_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1440_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1440,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1441","image_path":"images/combination_1441.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1441_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1441_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1441_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1441_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1441_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1441,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1442","image_path":"images/combination_1442.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1442_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1442_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1442_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1442_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1442_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1442,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1443","image_path":"images/combination_1443.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1443_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1443_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1443_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1443_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1443_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1443,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[593,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1444","image_path":"images/combination_1444.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1444_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1444_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1444_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1444_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1444_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1444,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2],[3,3],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1445","image_path":"images/combination_1445.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1445_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1445_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1445_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1445_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1445_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1445,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[571,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1446","image_path":"images/combination_1446.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1446_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1446_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1446_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":"combination_1446_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1446_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1446,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[555,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1447","image_path":"images/combination_1447.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1447_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1447_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1447_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1447_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1447_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1447,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[577,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1448","image_path":"images/combination_1448.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1448_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1448_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1448_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":"combination_1448_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1448_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1448,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[556,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1449","image_path":"images/combination_1449.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1449_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1449_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1449_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":"combination_1449_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1449_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1449,"target_cell_count":6,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[585,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1450","image_path":"images/combination_1450.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1450_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1450_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1450_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1450_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1450_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1450,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[572,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1451","image_path":"images/combination_1451.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1451_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1451_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1451_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":"combination_1451_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1451_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1451,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[567,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1452","image_path":"images/combination_1452.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1452_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1452_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1452_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":"combination_1452_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1452_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1452,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1453","image_path":"images/combination_1453.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1453_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1453_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1453_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1453_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1453_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1453,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[596,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1454","image_path":"images/combination_1454.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1454_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1454_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1454_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":"combination_1454_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1454_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1454,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[584,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1455","image_path":"images/combination_1455.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1455_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1455_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1455_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":"combination_1455_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1455_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1455,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":6}],"canvas_size":[579,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1456","image_path":"images/combination_1456.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1456_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1456_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1456_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1456_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1456_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1456,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[571,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1457","image_path":"images/combination_1457.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1457_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1457_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1457_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1457_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1457_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1457,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1458","image_path":"images/combination_1458.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1458_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1458_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1458_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":"combination_1458_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1458_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1458,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[576,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1459","image_path":"images/combination_1459.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1459_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1459_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1459_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1459_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1459_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1459,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[593,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1460","image_path":"images/combination_1460.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1460_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1460_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1460_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1460_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1460_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1460,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[552,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1461","image_path":"images/combination_1461.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1461_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1461_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1461_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1461_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1461_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1461,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1462","image_path":"images/combination_1462.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1462_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1462_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1462_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":"combination_1462_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1462_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1462,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":6}],"canvas_size":[591,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1463","image_path":"images/combination_1463.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1463_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1463_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1463_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1463_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1463_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1463,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1464","image_path":"images/combination_1464.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1464_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1464_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1464_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1464_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1464_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1464,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,3],[0,4],[1,3],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10}],"canvas_size":[565,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1465","image_path":"images/combination_1465.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1465_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1465_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1465_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1465_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1465_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1465,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[589,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1466","image_path":"images/combination_1466.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1466_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1466_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1466_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1466_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1466_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1466,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[597,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1467","image_path":"images/combination_1467.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1467_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1467_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1467_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":"combination_1467_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1467_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1467,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[593,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1468","image_path":"images/combination_1468.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1468_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1468_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1468_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1468_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1468_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1468,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1469","image_path":"images/combination_1469.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1469_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1469_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_1469_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":"combination_1469_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1469_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1469,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1470","image_path":"images/combination_1470.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1470_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1470_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1470_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":"combination_1470_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1470_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1470,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7}],"canvas_size":[559,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1471","image_path":"images/combination_1471.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1471_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1471_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1471_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1471_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1471_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1471,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[564,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1472","image_path":"images/combination_1472.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1472_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1472_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_1472_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":"combination_1472_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1472_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1472,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1473","image_path":"images/combination_1473.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1473_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1473_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1473_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1473_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1473_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1473,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[553,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1474","image_path":"images/combination_1474.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1474_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1474_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1474_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1474_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1474_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1474,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[557,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1475","image_path":"images/combination_1475.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1475_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1475_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1475_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":"combination_1475_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1475_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1475,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1476","image_path":"images/combination_1476.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1476_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1476_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1476_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":"combination_1476_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1476_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1476,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9}],"canvas_size":[594,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1477","image_path":"images/combination_1477.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1477_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1477_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1477_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1477_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1477_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1477,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[587,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1478","image_path":"images/combination_1478.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1478_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1478_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1478_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1478_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1478_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1478,"target_cell_count":7,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[5,0],[5,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1],[5,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[553,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1479","image_path":"images/combination_1479.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1479_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1479_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1479_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":"combination_1479_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1479_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1479,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[595,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1480","image_path":"images/combination_1480.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1480_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1480_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1480_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":"combination_1480_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1480_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1480,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"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],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6}],"canvas_size":[551,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1481","image_path":"images/combination_1481.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1481_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1481_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1481_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":"combination_1481_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1481_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1481,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[555,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1482","image_path":"images/combination_1482.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1482_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1482_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1482_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1482_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1482_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1482,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[589,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1483","image_path":"images/combination_1483.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1483_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1483_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1483_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":"combination_1483_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1483_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1483,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[559,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1484","image_path":"images/combination_1484.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1484_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1484_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1484_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":"combination_1484_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1484_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1484,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[572,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1485","image_path":"images/combination_1485.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1485_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1485_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1485_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":"combination_1485_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1485_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1485,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[577,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1486","image_path":"images/combination_1486.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1486_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1486_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1486_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1486_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1486_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1486,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[3,0],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[561,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1487","image_path":"images/combination_1487.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1487_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1487_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1487_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":"combination_1487_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1487_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1487,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,1],[3,1],[4,0],[4,1],[4,2],[5,1],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[567,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1488","image_path":"images/combination_1488.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1488_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1488_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1488_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1488_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1488_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1488,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[577,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1489","image_path":"images/combination_1489.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1489_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1489_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1489_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":"combination_1489_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1489_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1489,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1490","image_path":"images/combination_1490.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1490_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1490_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1490_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1490_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1490_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1490,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[564,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1491","image_path":"images/combination_1491.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1491_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1491_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1491_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":"combination_1491_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1491_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1491,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[589,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1492","image_path":"images/combination_1492.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1492_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1492_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1492_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1492_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1492_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1492,"target_cell_count":9,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[563,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1493","image_path":"images/combination_1493.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1493_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1493_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1493_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1493_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1493_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1493,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[561,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1494","image_path":"images/combination_1494.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1494_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1494_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1494_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":"combination_1494_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1494_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1494,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[577,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1495","image_path":"images/combination_1495.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1495_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1495_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1495_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1495_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1495_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1495,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1496","image_path":"images/combination_1496.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1496_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1496_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1496_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":"combination_1496_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1496_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1496,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[555,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1497","image_path":"images/combination_1497.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1497_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1497_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1497_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1497_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1497_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1497,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[559,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1498","image_path":"images/combination_1498.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1498_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1498_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1498_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":"combination_1498_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1498_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1498,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1499","image_path":"images/combination_1499.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1499_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1499_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1499_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1499_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1499_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1499,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[569,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1500","image_path":"images/combination_1500.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1500_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1500_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_1500_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1500_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1500,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[590,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1501","image_path":"images/combination_1501.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1501_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1501_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1501_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":"combination_1501_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1501_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1501,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1502","image_path":"images/combination_1502.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1502_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1502_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1502_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":"combination_1502_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1502_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1502,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1],[4,2],[5,1],[6,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1503","image_path":"images/combination_1503.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1503_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1503_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1503_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1503_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1503_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1503,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1504","image_path":"images/combination_1504.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1504_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1504_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1504_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":"combination_1504_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1504_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1504,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[557,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1505","image_path":"images/combination_1505.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1505_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1505_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1505_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":"combination_1505_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1505_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1505,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[561,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1506","image_path":"images/combination_1506.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1506_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1506_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_1506_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":"combination_1506_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1506_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1506,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1507","image_path":"images/combination_1507.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1507_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1507_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1507_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":"combination_1507_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1507_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1507,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_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],[1,2],[1,3],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[569,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1508","image_path":"images/combination_1508.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1508_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1508_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1508_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1508_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1508_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1508,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1509","image_path":"images/combination_1509.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1509_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1509_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1509_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1509_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1509_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1509,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,1],[2,3],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3],[3,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[575,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1510","image_path":"images/combination_1510.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1510_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1510_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1510_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":"combination_1510_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1510_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1510,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[1,4],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[561,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1511","image_path":"images/combination_1511.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1511_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1511_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1511_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":"combination_1511_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1511_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1511,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[580,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1512","image_path":"images/combination_1512.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1512_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1512_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1512_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1512_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1512_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1512,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_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],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1513","image_path":"images/combination_1513.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1513_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1513_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1513_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1513_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1513_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1513,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1514","image_path":"images/combination_1514.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1514_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1514_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1514_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1514_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1514_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1514,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1515","image_path":"images/combination_1515.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1515_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1515_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1515_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":"combination_1515_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1515_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1515,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[564,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1516","image_path":"images/combination_1516.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1516_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1516_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1516_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1516_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1516_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1516,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[575,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1517","image_path":"images/combination_1517.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1517_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1517_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_1517_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1517_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1517,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[562,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1518","image_path":"images/combination_1518.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1518_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1518_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1518_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1518_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1518_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1518,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[565,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1519","image_path":"images/combination_1519.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1519_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1519_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1519_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":"combination_1519_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1519_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1519,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[576,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1520","image_path":"images/combination_1520.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1520_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1520_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1520_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1520_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1520_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1520,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[550,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1521","image_path":"images/combination_1521.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1521_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1521_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_1521_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":"combination_1521_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1521_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1521,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[588,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1522","image_path":"images/combination_1522.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1522_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1522_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1522_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":"combination_1522_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1522_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1522,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[561,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1523","image_path":"images/combination_1523.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1523_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1523_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1523_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":"combination_1523_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1523_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1523,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1524","image_path":"images/combination_1524.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1524_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1524_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1524_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":"combination_1524_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1524_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1524,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[569,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1525","image_path":"images/combination_1525.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1525_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1525_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1525_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1525_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1525_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1525,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1526","image_path":"images/combination_1526.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1526_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1526_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1526_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":"combination_1526_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1526_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1526,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_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],[1,1],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[589,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1527","image_path":"images/combination_1527.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1527_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1527_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1527_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1527_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1527_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1527,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[572,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1528","image_path":"images/combination_1528.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1528_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1528_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1528_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1528_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1528_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1528,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,4]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,4]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[571,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1529","image_path":"images/combination_1529.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1529_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1529_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1529_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1529_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1529_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1529,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[552,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1530","image_path":"images/combination_1530.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1530_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1530_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1530_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1530_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1530_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1530,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[595,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1531","image_path":"images/combination_1531.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1531_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1531_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1531_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":"combination_1531_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1531_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1531,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1532","image_path":"images/combination_1532.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1532_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1532_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1532_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":"combination_1532_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1532_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1532,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[588,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1533","image_path":"images/combination_1533.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1533_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1533_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1533_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1533_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1533_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1533,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1534","image_path":"images/combination_1534.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1534_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1534_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1534_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":"combination_1534_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1534_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1534,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[569,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1535","image_path":"images/combination_1535.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1535_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1535_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1535_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1535_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1535_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1535,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1536","image_path":"images/combination_1536.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1536_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1536_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1536_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1536_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1536_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1536,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[572,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1537","image_path":"images/combination_1537.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1537_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1537_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1537_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1537_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1537,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[567,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1538","image_path":"images/combination_1538.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1538_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1538_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1538_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":"combination_1538_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1538_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1538,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[551,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1539","image_path":"images/combination_1539.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1539_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1539_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1539_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":"combination_1539_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1539_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1539,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[552,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1540","image_path":"images/combination_1540.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1540_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1540_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1540_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":"combination_1540_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1540_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1540,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8}],"canvas_size":[570,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1541","image_path":"images/combination_1541.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1541_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1541_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_1541_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":"combination_1541_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1541_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1541,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1542","image_path":"images/combination_1542.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1542_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1542_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1542_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1542_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1542_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1542,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[556,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1543","image_path":"images/combination_1543.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1543_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1543_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1543_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":"combination_1543_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1543_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1543,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2],[3,3],[4,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[562,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1544","image_path":"images/combination_1544.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1544_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1544_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_1544_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1544_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1544,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[562,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1545","image_path":"images/combination_1545.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1545_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1545_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1545_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1545_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1545_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1545,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[558,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1546","image_path":"images/combination_1546.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1546_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1546_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1546_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1546_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1546_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1546,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_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],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[557,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1547","image_path":"images/combination_1547.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1547_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1547_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1547_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1547_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1547_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1547,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1548","image_path":"images/combination_1548.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1548_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1548_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1548_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1548_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1548_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1548,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[582,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1549","image_path":"images/combination_1549.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1549_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1549_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1549_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1549_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1549_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1549,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5}],"canvas_size":[588,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1550","image_path":"images/combination_1550.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1550_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1550_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1550_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":"combination_1550_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1550_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1550,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7}],"canvas_size":[599,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1551","image_path":"images/combination_1551.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1551_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1551_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1551_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":"combination_1551_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1551_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1551,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1552","image_path":"images/combination_1552.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1552_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1552_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1552_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1552_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1552_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1552,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[589,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1553","image_path":"images/combination_1553.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1553_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1553_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1553_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":"combination_1553_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1553_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1553,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[576,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1554","image_path":"images/combination_1554.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1554_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1554_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1554_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1554_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1554_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1554,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[572,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1555","image_path":"images/combination_1555.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1555_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1555_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1555_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":"combination_1555_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1555_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1555,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[572,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1556","image_path":"images/combination_1556.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1556_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1556_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1556_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1556_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1556_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1556,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":8}],"canvas_size":[554,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1557","image_path":"images/combination_1557.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1557_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1557_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1557_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1557_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1557_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1557,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[559,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1558","image_path":"images/combination_1558.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1558_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1558_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1558_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1558_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1558_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1558,"target_cell_count":8,"target_cells":[[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1559","image_path":"images/combination_1559.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1559_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1559_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1559_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1559_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1559_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1559,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[596,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1560","image_path":"images/combination_1560.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1560_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1560_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1560_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1560_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1560_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1560,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[598,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1561","image_path":"images/combination_1561.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1561_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1561_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1561_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1561_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1561_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1561,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[572,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1562","image_path":"images/combination_1562.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1562_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1562_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1562_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1562_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1562_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1562,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[587,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1563","image_path":"images/combination_1563.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1563_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1563_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1563_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":"combination_1563_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1563_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1563,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[556,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1564","image_path":"images/combination_1564.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1564_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1564_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1564_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1564_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1564_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1564,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[588,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1565","image_path":"images/combination_1565.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1565_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1565_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1565_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1565_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1565_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1565,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1566","image_path":"images/combination_1566.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1566_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1566_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1566_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":"combination_1566_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1566_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1566,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1567","image_path":"images/combination_1567.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1567_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1567_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1567_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1567_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1567_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1567,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[579,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1568","image_path":"images/combination_1568.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1568_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1568_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1568_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1568_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1568_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1568,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[595,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1569","image_path":"images/combination_1569.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1569_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1569_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1569_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1569_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1569_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1569,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":10}],"canvas_size":[554,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1570","image_path":"images/combination_1570.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1570_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1570_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1570_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1570_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1570_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1570,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7}],"canvas_size":[561,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1571","image_path":"images/combination_1571.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1571_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1571_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1571_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1571_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1571_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1571,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1572","image_path":"images/combination_1572.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1572_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1572_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1572_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":"combination_1572_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1572_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1572,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[591,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1573","image_path":"images/combination_1573.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1573_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1573_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1573_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":"combination_1573_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1573_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1573,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[580,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1574","image_path":"images/combination_1574.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1574_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1574_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1574_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":"combination_1574_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1574_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1574,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[564,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1575","image_path":"images/combination_1575.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1575_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1575_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1575_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":"combination_1575_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1575_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1575,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1576","image_path":"images/combination_1576.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1576_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1576_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1576_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1576_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1576_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1576,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,1]]],"total_cell_count":10}],"canvas_size":[600,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1577","image_path":"images/combination_1577.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1577_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1577_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1577_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1577_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1577_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1577,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[578,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1578","image_path":"images/combination_1578.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1578_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1578_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_1578_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1578_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1578,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1579","image_path":"images/combination_1579.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1579_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1579_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1579_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":"combination_1579_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1579_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1579,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9}],"canvas_size":[558,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1580","image_path":"images/combination_1580.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1580_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1580_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1580_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":"combination_1580_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1580_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1580,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[592,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1581","image_path":"images/combination_1581.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1581_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1581_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1581_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":"combination_1581_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1581_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1581,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[563,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1582","image_path":"images/combination_1582.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1582_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1582_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1582_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":"combination_1582_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1582_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1582,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[577,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1583","image_path":"images/combination_1583.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1583_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1583_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1583_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":"combination_1583_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1583_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1583,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":10}],"canvas_size":[571,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1584","image_path":"images/combination_1584.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1584_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1584_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1584_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":"combination_1584_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1584_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1584,"target_cell_count":10,"target_cells":[[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[588,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1585","image_path":"images/combination_1585.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1585_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1585_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1585_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1585_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1585_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1585,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[573,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1586","image_path":"images/combination_1586.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1586_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1586_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1586_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1586_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1586_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1586,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[555,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1587","image_path":"images/combination_1587.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1587_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1587_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1587_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1587_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1587_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1587,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[588,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1588","image_path":"images/combination_1588.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1588_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1588_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1588_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":"combination_1588_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1588_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1588,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1589","image_path":"images/combination_1589.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1589_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1589_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1589_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1589_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1589_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1589,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[552,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1590","image_path":"images/combination_1590.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1590_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1590_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1590_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1590_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1590_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1590,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1591","image_path":"images/combination_1591.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1591_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1591_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1591_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":"combination_1591_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1591_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1591,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[573,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1592","image_path":"images/combination_1592.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1592_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1592_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1592_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":"combination_1592_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1592_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1592,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]]],"total_cell_count":8}],"canvas_size":[577,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1593","image_path":"images/combination_1593.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1593_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1593_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1593_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":"combination_1593_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1593_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1593,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[584,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1594","image_path":"images/combination_1594.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1594_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1594_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1594_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":"combination_1594_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1594_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1594,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1],[5,0],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[565,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1595","image_path":"images/combination_1595.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1595_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1595_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1595_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":"combination_1595_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1595_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1595,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,1],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[557,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1596","image_path":"images/combination_1596.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1596_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1596_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1596_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1596_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1596_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1596,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1597","image_path":"images/combination_1597.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1597_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1597_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1597_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":"combination_1597_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1597_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1597,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[580,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1598","image_path":"images/combination_1598.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1598_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1598_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1598_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1598_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1598_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1598,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[584,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1599","image_path":"images/combination_1599.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1599_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1599_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1599_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1599_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1599_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1599,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":10}],"canvas_size":[550,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1600","image_path":"images/combination_1600.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1600_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1600_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1600_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1600_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1600_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1600,"target_cell_count":10,"target_cells":[[0,3],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1601","image_path":"images/combination_1601.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1601_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1601_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1601_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1601_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1601_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1601,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[567,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1602","image_path":"images/combination_1602.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1602_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1602_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1602_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1602_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1602_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1602,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,403],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1603","image_path":"images/combination_1603.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1603_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1603_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1603_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":"combination_1603_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1603_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1603,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[551,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1604","image_path":"images/combination_1604.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1604_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1604_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1604_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":"combination_1604_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1604_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1604,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[558,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1605","image_path":"images/combination_1605.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1605_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1605_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1605_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":"combination_1605_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1605_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1605,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3],[3,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1606","image_path":"images/combination_1606.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1606_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1606_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1606_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":"combination_1606_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1606_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1606,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1607","image_path":"images/combination_1607.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1607_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1607_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1607_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1607_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1607_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1607,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1608","image_path":"images/combination_1608.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1608_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1608_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1608_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1608_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1608_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1608,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[577,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1609","image_path":"images/combination_1609.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1609_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1609_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1609_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1609_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1609_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1609,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1610","image_path":"images/combination_1610.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1610_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1610_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1610_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":"combination_1610_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1610_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1610,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1611","image_path":"images/combination_1611.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1611_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1611_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1611_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1611_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1611_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1611,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1612","image_path":"images/combination_1612.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1612_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1612_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1612_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":"combination_1612_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1612_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1612,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[571,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1613","image_path":"images/combination_1613.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1613_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1613_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1613_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1613_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1613_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1613,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1614","image_path":"images/combination_1614.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1614_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1614_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1614_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1614_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1614_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1614,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[572,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1615","image_path":"images/combination_1615.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1615_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1615_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1615_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":"combination_1615_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1615_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1615,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1616","image_path":"images/combination_1616.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1616_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1616_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1616_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":"combination_1616_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1616_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1616,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1617","image_path":"images/combination_1617.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1617_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1617_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1617_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":"combination_1617_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1617_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1617,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[594,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1618","image_path":"images/combination_1618.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1618_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1618_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1618_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1618_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1618_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1618,"target_cell_count":8,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":8}],"canvas_size":[553,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1619","image_path":"images/combination_1619.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1619_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1619_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1619_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1619_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1619_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1619,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[555,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1620","image_path":"images/combination_1620.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1620_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1620_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1620_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":"combination_1620_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1620_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1620,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[560,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1621","image_path":"images/combination_1621.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1621_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1621_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1621_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1621_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1621_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1621,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[578,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1622","image_path":"images/combination_1622.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1622_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1622_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1622_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":"combination_1622_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1622_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1622,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[594,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1623","image_path":"images/combination_1623.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1623_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1623_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1623_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1623_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1623_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1623,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[565,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1624","image_path":"images/combination_1624.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1624_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1624_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1624_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1624_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1624_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1624,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2],[5,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1],[5,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[570,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1625","image_path":"images/combination_1625.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1625_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1625_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1625_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1625_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1625_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1625,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[3,3],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[570,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1626","image_path":"images/combination_1626.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1626_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1626_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1626_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1626_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1626_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1626,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[572,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1627","image_path":"images/combination_1627.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1627_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1627_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1627_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":"combination_1627_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1627_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1627,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1628","image_path":"images/combination_1628.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1628_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1628_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1628_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1628_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1628_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1628,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":10}],"canvas_size":[589,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1629","image_path":"images/combination_1629.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1629_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1629_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1629_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1629_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1629_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1629,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[553,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1630","image_path":"images/combination_1630.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1630_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1630_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1630_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1630_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1630_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1630,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1631","image_path":"images/combination_1631.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1631_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1631_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1631_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1631_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1631_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1631,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1632","image_path":"images/combination_1632.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1632_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1632_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1632_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":"combination_1632_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1632_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1632,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[584,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1633","image_path":"images/combination_1633.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1633_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1633_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1633_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1633_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1633_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1633,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[598,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1634","image_path":"images/combination_1634.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1634_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1634_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1634_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1634_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1634_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1634,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[554,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1635","image_path":"images/combination_1635.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1635_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1635_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1635_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":"combination_1635_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1635_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1635,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[558,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1636","image_path":"images/combination_1636.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1636_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1636_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1636_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1636_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1636_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1636,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7}],"canvas_size":[570,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1637","image_path":"images/combination_1637.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1637_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1637_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1637_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":"combination_1637_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1637_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1637,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0],[4,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0],[4,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10}],"canvas_size":[597,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1638","image_path":"images/combination_1638.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1638_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1638_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1638_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":"combination_1638_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1638_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1638,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,1],[4,1],[4,2],[5,0],[5,1],[6,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1639","image_path":"images/combination_1639.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1639_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1639_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1639_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":"combination_1639_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1639_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1639,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[600,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1640","image_path":"images/combination_1640.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1640_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1640_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1640_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1640_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1640_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1640,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":8}],"canvas_size":[600,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1641","image_path":"images/combination_1641.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1641_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1641_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1641_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1641_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1641_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1641,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1642","image_path":"images/combination_1642.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1642_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1642_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1642_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":"combination_1642_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1642_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1642,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4],[2,4],[2,5]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1643","image_path":"images/combination_1643.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1643_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1643_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1643_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1643_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1643_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1643,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1644","image_path":"images/combination_1644.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1644_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1644_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_1644_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1644_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1644,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[594,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1645","image_path":"images/combination_1645.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1645_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1645_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1645_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1645_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1645_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1645,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[576,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1646","image_path":"images/combination_1646.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1646_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1646_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1646_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":"combination_1646_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1646_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1646,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]]],"total_cell_count":8}],"canvas_size":[578,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1647","image_path":"images/combination_1647.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1647_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1647_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1647_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1647_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1647_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1647,"target_cell_count":8,"target_cells":[[0,0],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[550,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1648","image_path":"images/combination_1648.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1648_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1648_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1648_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1648_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1648_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1648,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1649","image_path":"images/combination_1649.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1649_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1649_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_1649_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1649_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1649,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1650","image_path":"images/combination_1650.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1650_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1650_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1650_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":"combination_1650_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1650_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1650,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[550,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1651","image_path":"images/combination_1651.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1651_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1651_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1651_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1651_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1651_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1651,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[572,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1652","image_path":"images/combination_1652.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1652_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1652_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1652_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1652_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1652_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1652,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":10}],"canvas_size":[553,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1653","image_path":"images/combination_1653.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1653_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1653_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1653_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1653_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1653_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1653,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":5}],"canvas_size":[565,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1654","image_path":"images/combination_1654.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1654_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1654_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1654_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1654_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1654_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1654,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[582,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1655","image_path":"images/combination_1655.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1655_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1655_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1655_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1655_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1655_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1655,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1656","image_path":"images/combination_1656.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1656_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1656_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1656_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1656_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1656_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1656,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[595,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1657","image_path":"images/combination_1657.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1657_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1657_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1657_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1657_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1657_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1657,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[595,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1658","image_path":"images/combination_1658.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1658_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1658_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1658_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":"combination_1658_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1658_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1658,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[578,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1659","image_path":"images/combination_1659.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1659_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1659_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1659_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1659_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1659_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1659,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[598,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1660","image_path":"images/combination_1660.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1660_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1660_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1660_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":"combination_1660_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1660_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1660,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1661","image_path":"images/combination_1661.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1661_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1661_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1661_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":"combination_1661_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1661_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1661,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[594,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1662","image_path":"images/combination_1662.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1662_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1662_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1662_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1662_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1662_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1662,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[591,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1663","image_path":"images/combination_1663.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1663_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1663_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1663_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1663_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1663_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1663,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[597,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1664","image_path":"images/combination_1664.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1664_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1664_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1664_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":"combination_1664_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1664_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1664,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[584,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1665","image_path":"images/combination_1665.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1665_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1665_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1665_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1665_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1665_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1665,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,5],[2,3],[2,4],[2,5]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[1,4]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1666","image_path":"images/combination_1666.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1666_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1666_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1666_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1666_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1666_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1666,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[581,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1667","image_path":"images/combination_1667.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1667_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1667_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1667_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":"combination_1667_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1667_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1667,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[587,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1668","image_path":"images/combination_1668.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1668_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1668_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1668_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":"combination_1668_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1668_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1668,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[564,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1669","image_path":"images/combination_1669.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1669_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1669_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1669_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":"combination_1669_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1669_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1669,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1670","image_path":"images/combination_1670.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1670_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1670_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1670_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1670_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1670_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1670,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1671","image_path":"images/combination_1671.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1671_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1671_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1671_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1671_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1671_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1671,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7}],"canvas_size":[584,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1672","image_path":"images/combination_1672.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1672_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1672_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1672_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":"combination_1672_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1672_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1672,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[569,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1673","image_path":"images/combination_1673.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1673_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1673_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1673_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":"combination_1673_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1673_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1673,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1674","image_path":"images/combination_1674.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1674_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1674_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1674_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1674_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1674_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1674,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1675","image_path":"images/combination_1675.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1675_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1675_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1675_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":"combination_1675_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1675_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1675,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1676","image_path":"images/combination_1676.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1676_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1676_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1676_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":"combination_1676_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1676_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1676,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":8}],"canvas_size":[594,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1677","image_path":"images/combination_1677.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1677_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1677_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1677_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":"combination_1677_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1677_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1677,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":8}],"canvas_size":[566,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1678","image_path":"images/combination_1678.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1678_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1678_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1678_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1678_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1678_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1678,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"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]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[555,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1679","image_path":"images/combination_1679.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1679_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1679_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1679_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1679_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1679_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1679,"target_cell_count":7,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[568,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1680","image_path":"images/combination_1680.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1680_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1680_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1680_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1680_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1680_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1680,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[567,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1681","image_path":"images/combination_1681.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1681_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1681_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1681_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":"combination_1681_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1681_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1681,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1682","image_path":"images/combination_1682.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1682_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1682_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1682_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":"combination_1682_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1682_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1682,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[551,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1683","image_path":"images/combination_1683.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1683_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1683_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1683_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1683_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1683_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1683,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[580,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1684","image_path":"images/combination_1684.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1684_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1684_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1684_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":"combination_1684_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1684_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1684,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[585,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1685","image_path":"images/combination_1685.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1685_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1685_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1685_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1685_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1685_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1685,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[563,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1686","image_path":"images/combination_1686.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1686_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1686_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1686_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1686_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1686_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1686,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6}],"canvas_size":[592,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1687","image_path":"images/combination_1687.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1687_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1687_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1687_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1687_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1687_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1687,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1688","image_path":"images/combination_1688.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1688_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1688_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1688_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1688_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1688_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1688,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[586,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1689","image_path":"images/combination_1689.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1689_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1689_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1689_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1689_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1689_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1689,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8}],"canvas_size":[554,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1690","image_path":"images/combination_1690.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1690_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1690_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1690_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":"combination_1690_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1690_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1690,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[566,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1691","image_path":"images/combination_1691.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1691_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1691_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1691_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":"combination_1691_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1691_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1691,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[600,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1692","image_path":"images/combination_1692.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1692_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1692_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1692_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1692_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1692_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1692,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[596,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1693","image_path":"images/combination_1693.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1693_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1693_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1693_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1693_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1693_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1693,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[590,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1694","image_path":"images/combination_1694.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1694_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1694_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1694_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":"combination_1694_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1694_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1694,"target_cell_count":7,"target_cells":[[0,0],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[555,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1695","image_path":"images/combination_1695.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1695_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1695_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1695_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1695_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1695_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1695,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1696","image_path":"images/combination_1696.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1696_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1696_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1696_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":"combination_1696_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1696_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1696,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[595,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1697","image_path":"images/combination_1697.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1697_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1697_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1697_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1697_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1697_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1697,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[576,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1698","image_path":"images/combination_1698.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1698_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1698_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1698_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":"combination_1698_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1698_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1698,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[569,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1699","image_path":"images/combination_1699.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1699_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1699_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1699_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1699_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1699_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1699,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_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],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[577,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1700","image_path":"images/combination_1700.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1700_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1700_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1700_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":"combination_1700_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1700_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1700,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[581,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1701","image_path":"images/combination_1701.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1701_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1701_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1701_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1701_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1701_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1701,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[576,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1702","image_path":"images/combination_1702.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1702_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1702_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1702_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":"combination_1702_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1702_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1702,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1703","image_path":"images/combination_1703.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1703_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1703_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1703_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":"combination_1703_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1703_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1703,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[583,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1704","image_path":"images/combination_1704.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1704_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1704_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1704_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1704_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1704_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1704,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[597,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1705","image_path":"images/combination_1705.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1705_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1705_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1705_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1705_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1705_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1705,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[578,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1706","image_path":"images/combination_1706.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1706_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1706_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1706_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1706_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1706_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1706,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[561,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1707","image_path":"images/combination_1707.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1707_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1707_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1707_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":"combination_1707_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1707_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1707,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[570,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1708","image_path":"images/combination_1708.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1708_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1708_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1708_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":"combination_1708_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1708_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1708,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[3,3],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[589,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1709","image_path":"images/combination_1709.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1709_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1709_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1709_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":"combination_1709_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1709_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1709,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[574,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1710","image_path":"images/combination_1710.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1710_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1710_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1710_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1710_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1710_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1710,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[599,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1711","image_path":"images/combination_1711.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1711_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1711_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1711_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":"combination_1711_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1711_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1711,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[596,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1712","image_path":"images/combination_1712.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1712_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1712_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1712_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":"combination_1712_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1712_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1712,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[595,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1713","image_path":"images/combination_1713.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1713_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1713_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1713_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":"combination_1713_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1713_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1713,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1714","image_path":"images/combination_1714.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1714_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1714_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1714_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":"combination_1714_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1714_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1714,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[582,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1715","image_path":"images/combination_1715.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1715_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1715_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1715_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1715_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1715_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1715,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[550,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1716","image_path":"images/combination_1716.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1716_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1716_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1716_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1716_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1716_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1716,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[599,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1717","image_path":"images/combination_1717.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1717_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1717_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1717_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":"combination_1717_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1717_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1717,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[576,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1718","image_path":"images/combination_1718.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1718_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1718_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1718_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":"combination_1718_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1718_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1718,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[582,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1719","image_path":"images/combination_1719.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1719_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1719_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1719_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":"combination_1719_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1719_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1719,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[569,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1720","image_path":"images/combination_1720.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1720_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1720_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1720_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1720_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1720_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1720,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2],[3,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1721","image_path":"images/combination_1721.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1721_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1721_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1721_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1721_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1721_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1721,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":10}],"canvas_size":[580,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1722","image_path":"images/combination_1722.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1722_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1722_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1722_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":"combination_1722_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1722_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1722,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[567,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1723","image_path":"images/combination_1723.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1723_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1723_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1723_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":"combination_1723_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1723_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1723,"target_cell_count":7,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[555,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1724","image_path":"images/combination_1724.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1724_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1724_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1724_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1724_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1724_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1724,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[568,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1725","image_path":"images/combination_1725.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1725_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1725_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1725_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1725_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1725_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1725,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1726","image_path":"images/combination_1726.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1726_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1726_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_1726_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1726_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1726,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[593,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1727","image_path":"images/combination_1727.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1727_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1727_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1727_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":"combination_1727_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1727_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1727,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3],[2,4],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[574,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1728","image_path":"images/combination_1728.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1728_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1728_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1728_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":"combination_1728_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1728_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1728,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1729","image_path":"images/combination_1729.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1729_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1729_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1729_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":"combination_1729_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1729_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1729,"target_cell_count":9,"target_cells":[[0,4],[1,4],[2,2],[2,3],[2,4],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1730","image_path":"images/combination_1730.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1730_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1730_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1730_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":"combination_1730_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1730_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1730,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1731","image_path":"images/combination_1731.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1731_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1731_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1731_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":"combination_1731_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1731_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1731,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[565,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1732","image_path":"images/combination_1732.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1732_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1732_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1732_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":"combination_1732_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1732_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1732,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1],[5,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1],[5,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[558,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1733","image_path":"images/combination_1733.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1733_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1733_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1733_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":"combination_1733_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1733_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1733,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3],[4,1],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":7}],"canvas_size":[557,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1734","image_path":"images/combination_1734.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1734_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1734_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1734_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1734_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1734_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1734,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[577,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1735","image_path":"images/combination_1735.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1735_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1735_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_1735_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1735_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1735,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1736","image_path":"images/combination_1736.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1736_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1736_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1736_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1736_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1736_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1736,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1737","image_path":"images/combination_1737.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1737_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1737_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1737_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":"combination_1737_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1737_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1737,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[583,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1738","image_path":"images/combination_1738.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1738_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1738_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1738_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":"combination_1738_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1738_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1738,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[565,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1739","image_path":"images/combination_1739.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1739_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1739_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1739_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1739_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1739_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1739,"target_cell_count":9,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[596,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1740","image_path":"images/combination_1740.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1740_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1740_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1740_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1740_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1740_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1740,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[595,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1741","image_path":"images/combination_1741.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1741_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1741_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1741_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":"combination_1741_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1741_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1741,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1742","image_path":"images/combination_1742.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1742_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1742_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1742_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":"combination_1742_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1742_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1742,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[592,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1743","image_path":"images/combination_1743.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1743_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1743_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1743_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1743_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1743_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1743,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[569,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1744","image_path":"images/combination_1744.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1744_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1744_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1744_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":"combination_1744_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1744_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1744,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[569,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1745","image_path":"images/combination_1745.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1745_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1745_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1745_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1745_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1745_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1745,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[564,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1746","image_path":"images/combination_1746.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1746_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1746_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1746_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":"combination_1746_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1746_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1746,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[579,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1747","image_path":"images/combination_1747.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1747_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1747_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1747_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1747_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1747_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1747,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1748","image_path":"images/combination_1748.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1748_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1748_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1748_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":"combination_1748_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1748_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1748,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[599,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1749","image_path":"images/combination_1749.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1749_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1749_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1749_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1749_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1749_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1749,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6}],"canvas_size":[573,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1750","image_path":"images/combination_1750.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1750_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1750_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1750_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1750_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1750_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1750,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[550,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1751","image_path":"images/combination_1751.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1751_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1751_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1751_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1751_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1751_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1751,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[563,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1752","image_path":"images/combination_1752.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1752_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1752_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1752_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":"combination_1752_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1752_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1752,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[553,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1753","image_path":"images/combination_1753.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1753_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1753_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1753_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1753_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1753_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1753,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[562,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1754","image_path":"images/combination_1754.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1754_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1754_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1754_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1754_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1754_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1754,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[598,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1755","image_path":"images/combination_1755.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1755_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1755_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1755_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":"combination_1755_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1755_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1755,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[598,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1756","image_path":"images/combination_1756.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1756_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1756_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1756_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1756_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1756_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1756,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9}],"canvas_size":[593,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1757","image_path":"images/combination_1757.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1757_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1757_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1757_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1757_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1757_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1757,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[559,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1758","image_path":"images/combination_1758.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1758_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1758_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1758_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1758_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1758_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1758,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[598,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1759","image_path":"images/combination_1759.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1759_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1759_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1759_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1759_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1759_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1759,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[582,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1760","image_path":"images/combination_1760.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1760_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1760_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1760_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":"combination_1760_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1760_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1760,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[555,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1761","image_path":"images/combination_1761.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1761_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1761_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1761_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":"combination_1761_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1761_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1761,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1762","image_path":"images/combination_1762.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1762_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1762_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1762_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1762_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1762_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1762,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[595,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1763","image_path":"images/combination_1763.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1763_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1763_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_1763_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1763_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1763,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1764","image_path":"images/combination_1764.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1764_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1764_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1764_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1764_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1764_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1764,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[563,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1765","image_path":"images/combination_1765.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1765_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1765_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1765_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":"combination_1765_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1765_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1765,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[562,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1766","image_path":"images/combination_1766.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1766_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1766_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1766_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":"combination_1766_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1766_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1766,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[596,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1767","image_path":"images/combination_1767.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1767_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1767_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_1767_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1767_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1767,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1768","image_path":"images/combination_1768.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1768_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1768_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1768_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":"combination_1768_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1768_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1768,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[551,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1769","image_path":"images/combination_1769.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1769_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1769_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1769_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1769_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1769_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1769,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[571,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1770","image_path":"images/combination_1770.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1770_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1770_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1770_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1770_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1770_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1770,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[560,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1771","image_path":"images/combination_1771.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1771_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1771_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1771_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":"combination_1771_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1771_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1771,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0],[0,1],[0,2]]],"total_cell_count":10}],"canvas_size":[562,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1772","image_path":"images/combination_1772.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1772_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1772_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1772_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1772_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1772_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1772,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[576,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1773","image_path":"images/combination_1773.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1773_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1773_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1773_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":"combination_1773_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1773_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1773,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[571,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1774","image_path":"images/combination_1774.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1774_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1774_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1774_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":"combination_1774_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1774_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1774,"target_cell_count":9,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1775","image_path":"images/combination_1775.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1775_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1775_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1775_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1775_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1775_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1775,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1776","image_path":"images/combination_1776.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1776_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1776_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1776_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1776_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1776_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1776,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1777","image_path":"images/combination_1777.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1777_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1777_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1777_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":"combination_1777_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1777_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1777,"target_cell_count":7,"target_cells":[[0,2],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[553,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1778","image_path":"images/combination_1778.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1778_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1778_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1778_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":"combination_1778_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1778_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1778,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[582,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1779","image_path":"images/combination_1779.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1779_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1779_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1779_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":"combination_1779_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1779_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1779,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1780","image_path":"images/combination_1780.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1780_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1780_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1780_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1780_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1780_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1780,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":8}],"canvas_size":[555,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1781","image_path":"images/combination_1781.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1781_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1781_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1781_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1781_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1781_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1781,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":5}],"canvas_size":[581,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1782","image_path":"images/combination_1782.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1782_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1782_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1782_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1782_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1782_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1782,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[581,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1783","image_path":"images/combination_1783.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1783_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1783_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1783_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1783_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1783_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1783,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[553,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1784","image_path":"images/combination_1784.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1784_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1784_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1784_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":"combination_1784_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1784_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1784,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[600,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1785","image_path":"images/combination_1785.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1785_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1785_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1785_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":"combination_1785_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1785_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1785,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":7}],"canvas_size":[583,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1786","image_path":"images/combination_1786.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1786_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1786_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1786_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":"combination_1786_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1786_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1786,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[560,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1787","image_path":"images/combination_1787.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1787_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1787_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1787_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1787_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1787_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1787,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1788","image_path":"images/combination_1788.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1788_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1788_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1788_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1788_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1788_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1788,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1789","image_path":"images/combination_1789.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1789_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1789_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1789_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1789_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1789_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1789,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":7}],"canvas_size":[560,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1790","image_path":"images/combination_1790.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1790_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1790_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1790_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1790_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1790_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1790,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[572,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1791","image_path":"images/combination_1791.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1791_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1791_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1791_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1791_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1791_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1791,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[1,4],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]],"total_cell_count":9}],"canvas_size":[597,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1792","image_path":"images/combination_1792.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1792_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1792_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1792_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1792_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1792_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1792,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[551,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1793","image_path":"images/combination_1793.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1793_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1793_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1793_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":"combination_1793_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1793_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1793,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[570,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1794","image_path":"images/combination_1794.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1794_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1794_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1794_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1794_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1794_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1794,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[556,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1795","image_path":"images/combination_1795.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1795_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1795_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1795_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1795_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1795_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1795,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[580,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1796","image_path":"images/combination_1796.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1796_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1796_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1796_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1796_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1796_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1796,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[568,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1797","image_path":"images/combination_1797.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1797_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1797_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1797_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1797_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1797_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1797,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[580,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1798","image_path":"images/combination_1798.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1798_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1798_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1798_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":"combination_1798_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1798_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1798,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[565,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1799","image_path":"images/combination_1799.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1799_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1799_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1799_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":"combination_1799_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1799_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1799,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1800","image_path":"images/combination_1800.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1800_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1800_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1800_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1800_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1800_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1800,"target_cell_count":6,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1801","image_path":"images/combination_1801.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1801_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1801_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1801_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":"combination_1801_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1801_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1801,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[592,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1802","image_path":"images/combination_1802.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1802_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1802_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1802_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":"combination_1802_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1802_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1802,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1],[4,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[583,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1803","image_path":"images/combination_1803.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1803_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1803_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1803_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1803_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1803_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1803,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1804","image_path":"images/combination_1804.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1804_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1804_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1804_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1804_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1804_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1804,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1805","image_path":"images/combination_1805.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1805_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1805_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1805_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1805_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1805_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1805,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1806","image_path":"images/combination_1806.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1806_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1806_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1806_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":"combination_1806_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1806_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1806,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1807","image_path":"images/combination_1807.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1807_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1807_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1807_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1807_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1807_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1807,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[550,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1808","image_path":"images/combination_1808.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1808_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1808_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1808_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":"combination_1808_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1808_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1808,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[598,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1809","image_path":"images/combination_1809.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1809_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1809_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1809_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1809_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1809_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1809,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[554,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1810","image_path":"images/combination_1810.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1810_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1810_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1810_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":"combination_1810_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1810_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1810,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]]],"total_cell_count":10}],"canvas_size":[585,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1811","image_path":"images/combination_1811.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1811_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1811_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1811_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1811_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1811_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1811,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[585,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1812","image_path":"images/combination_1812.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1812_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1812_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1812_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1812_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1812_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1812,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2],[4,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1813","image_path":"images/combination_1813.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1813_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1813_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1813_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":"combination_1813_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1813_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1813,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"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],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[599,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1814","image_path":"images/combination_1814.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1814_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1814_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1814_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1814_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1814_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1814,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[553,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1815","image_path":"images/combination_1815.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1815_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1815_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1815_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":"combination_1815_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1815_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1815,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[568,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1816","image_path":"images/combination_1816.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1816_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1816_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1816_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":"combination_1816_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1816_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1816,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[584,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1817","image_path":"images/combination_1817.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1817_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1817_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_1817_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1817_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1817,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[560,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1818","image_path":"images/combination_1818.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1818_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1818_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1818_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1818_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1818_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1818,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[578,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1819","image_path":"images/combination_1819.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1819_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1819_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1819_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1819_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1819_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1819,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[559,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1820","image_path":"images/combination_1820.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1820_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1820_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1820_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":"combination_1820_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1820_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1820,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[572,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1821","image_path":"images/combination_1821.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1821_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1821_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1821_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":"combination_1821_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1821_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1821,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[600,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1822","image_path":"images/combination_1822.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1822_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1822_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1822_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1822_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1822_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1822,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[567,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1823","image_path":"images/combination_1823.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1823_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1823_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1823_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":"combination_1823_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1823_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1823,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[564,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1824","image_path":"images/combination_1824.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1824_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1824_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1824_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1824_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1824_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1824,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[4,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1825","image_path":"images/combination_1825.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1825_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1825_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1825_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1825_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1825_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1825,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1826","image_path":"images/combination_1826.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1826_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1826_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1826_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1826_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1826_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1826,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[567,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1827","image_path":"images/combination_1827.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1827_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1827_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1827_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":"combination_1827_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1827_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1827,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[591,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1828","image_path":"images/combination_1828.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1828_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1828_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1828_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":"combination_1828_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1828_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1828,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1829","image_path":"images/combination_1829.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1829_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1829_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1829_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1829_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1829_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1829,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[589,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1830","image_path":"images/combination_1830.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1830_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1830_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1830_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":"combination_1830_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1830_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1830,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[582,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1831","image_path":"images/combination_1831.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1831_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1831_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1831_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":"combination_1831_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1831_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1831,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[581,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1832","image_path":"images/combination_1832.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1832_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1832_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1832_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1832_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1832_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1832,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1],[4,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[588,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1833","image_path":"images/combination_1833.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1833_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1833_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1833_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1833_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1833_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1833,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[574,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1834","image_path":"images/combination_1834.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1834_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1834_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1834_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":"combination_1834_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1834_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1834,"target_cell_count":8,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6}],"canvas_size":[600,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1835","image_path":"images/combination_1835.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1835_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1835_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1835_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":"combination_1835_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1835_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1835,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[563,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1836","image_path":"images/combination_1836.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1836_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1836_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1836_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1836_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1836_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1836,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[582,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1837","image_path":"images/combination_1837.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1837_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1837_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1837_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1837_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1837_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1837,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[560,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1838","image_path":"images/combination_1838.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1838_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1838_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1838_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1838_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1838,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[553,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1839","image_path":"images/combination_1839.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1839_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1839_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1839_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":"combination_1839_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1839_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1839,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[579,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1840","image_path":"images/combination_1840.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1840_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1840_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1840_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1840_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1840_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1840,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1841","image_path":"images/combination_1841.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1841_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1841_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1841_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":"combination_1841_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1841_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1841,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4],[2,4]],[[0,0],[0,1],[1,1]]],"total_cell_count":10}],"canvas_size":[560,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1842","image_path":"images/combination_1842.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1842_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1842_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1842_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":"combination_1842_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1842_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1842,"target_cell_count":10,"target_cells":[[0,0],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[575,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1843","image_path":"images/combination_1843.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1843_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1843_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1843_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1843_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1843_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1843,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":9}],"canvas_size":[583,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1844","image_path":"images/combination_1844.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1844_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1844_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1844_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1844_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1844_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1844,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,3],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[555,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1845","image_path":"images/combination_1845.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1845_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1845_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1845_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1845_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1845_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1845,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[600,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1846","image_path":"images/combination_1846.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1846_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1846_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1846_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":"combination_1846_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1846_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1846,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1847","image_path":"images/combination_1847.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1847_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1847_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1847_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1847_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1847,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9}],"canvas_size":[580,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1848","image_path":"images/combination_1848.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1848_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1848_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1848_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":"combination_1848_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1848_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1848,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1],[4,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]]],"total_cell_count":9}],"canvas_size":[568,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1849","image_path":"images/combination_1849.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1849_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1849_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1849_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1849_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1849_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1849,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10}],"canvas_size":[596,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1850","image_path":"images/combination_1850.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1850_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1850_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1850_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":"combination_1850_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1850_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1850,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[575,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1851","image_path":"images/combination_1851.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1851_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1851_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1851_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1851_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1851_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1851,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[1,5],[1,6]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7]],[[0,0]]],"total_cell_count":10}],"canvas_size":[554,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1852","image_path":"images/combination_1852.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1852_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1852_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_1852_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1852_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1852,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]]],"total_cell_count":9}],"canvas_size":[565,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1853","image_path":"images/combination_1853.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1853_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1853_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1853_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1853_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1853_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1853,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[571,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1854","image_path":"images/combination_1854.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1854_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1854_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1854_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1854_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1854_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1854,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":10}],"canvas_size":[568,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1855","image_path":"images/combination_1855.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1855_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1855_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1855_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1855_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1855_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1855,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[593,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1856","image_path":"images/combination_1856.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1856_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1856_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1856_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1856_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1856_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1856,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[562,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1857","image_path":"images/combination_1857.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1857_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1857_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1857_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1857_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1857_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1857,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8}],"canvas_size":[586,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1858","image_path":"images/combination_1858.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1858_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1858_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1858_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":"combination_1858_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1858_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1858,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10}],"canvas_size":[597,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1859","image_path":"images/combination_1859.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1859_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1859_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1859_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1859_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1859_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1859,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":10}],"canvas_size":[589,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1860","image_path":"images/combination_1860.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1860_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1860_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1860_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1860_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1860_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1860,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1861","image_path":"images/combination_1861.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1861_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1861_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1861_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1861_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1861_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1861,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[567,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1862","image_path":"images/combination_1862.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1862_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1862_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1862_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":"combination_1862_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1862_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1862,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1863","image_path":"images/combination_1863.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1863_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1863_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1863_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":"combination_1863_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1863_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1863,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[554,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1864","image_path":"images/combination_1864.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1864_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1864_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1864_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":"combination_1864_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1864_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1864,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1865","image_path":"images/combination_1865.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1865_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1865_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1865_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":"combination_1865_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1865_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1865,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1866","image_path":"images/combination_1866.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1866_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1866_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"A","question_id":"combination_1866_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1866_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1866,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1867","image_path":"images/combination_1867.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1867_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1867_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_1867_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1867_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1867,"target_cell_count":9,"target_cells":[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[588,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1868","image_path":"images/combination_1868.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1868_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1868_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1868_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1868_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1868_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1868,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[599,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1869","image_path":"images/combination_1869.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1869_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1869_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1869_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1869_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1869_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1869,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[571,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1870","image_path":"images/combination_1870.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1870_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1870_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1870_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":"combination_1870_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1870_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1870,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1871","image_path":"images/combination_1871.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1871_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1871_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1871_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":"combination_1871_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1871_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1871,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1872","image_path":"images/combination_1872.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1872_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1872_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1872_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":"combination_1872_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1872_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1872,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[600,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1873","image_path":"images/combination_1873.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1873_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1873_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1873_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":"combination_1873_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1873_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1873,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1874","image_path":"images/combination_1874.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1874_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1874_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1874_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1874_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1874_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1874,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[565,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1875","image_path":"images/combination_1875.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1875_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1875_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1875_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":"combination_1875_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1875_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1875,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1876","image_path":"images/combination_1876.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1876_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1876_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1876_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1876_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1876_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1876,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[559,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1877","image_path":"images/combination_1877.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1877_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1877_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1877_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":"combination_1877_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1877_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1877,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1878","image_path":"images/combination_1878.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1878_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1878_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1878_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":"combination_1878_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1878_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1878,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[598,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1879","image_path":"images/combination_1879.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1879_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1879_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1879_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":"combination_1879_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1879_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1879,"target_cell_count":7,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[599,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1880","image_path":"images/combination_1880.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1880_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1880_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1880_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1880_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1880_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1880,"target_cell_count":10,"target_cells":[[0,0],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1881","image_path":"images/combination_1881.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1881_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1881_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1881_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":"combination_1881_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1881_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1881,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1882","image_path":"images/combination_1882.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1882_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1882_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1882_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1882_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1882_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1882,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[593,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1883","image_path":"images/combination_1883.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1883_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1883_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1883_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1883_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1883_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1883,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[557,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1884","image_path":"images/combination_1884.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1884_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1884_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1884_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1884_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1884_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1884,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[592,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1885","image_path":"images/combination_1885.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1885_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1885_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1885_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":"combination_1885_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1885_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1885,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[552,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1886","image_path":"images/combination_1886.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1886_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1886_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1886_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1886_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1886_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1886,"target_cell_count":8,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[572,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1887","image_path":"images/combination_1887.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1887_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1887_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1887_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1887_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1887_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1887,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[588,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1888","image_path":"images/combination_1888.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1888_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1888_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1888_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":"combination_1888_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1888_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1888,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[569,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1889","image_path":"images/combination_1889.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1889_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1889_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1889_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1889_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1889_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1889,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[574,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1890","image_path":"images/combination_1890.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1890_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1890_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1890_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1890_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1890_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1890,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[595,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1891","image_path":"images/combination_1891.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1891_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1891_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1891_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1891_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1891_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1891,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[590,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1892","image_path":"images/combination_1892.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1892_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1892_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1892_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1892_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1892_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1892,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]],"total_cell_count":10}],"canvas_size":[597,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1893","image_path":"images/combination_1893.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1893_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1893_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1893_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1893_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1893_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1893,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[599,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1894","image_path":"images/combination_1894.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1894_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1894_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1894_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":"combination_1894_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1894_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1894,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[569,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1895","image_path":"images/combination_1895.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1895_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1895_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1895_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":"combination_1895_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1895_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1895,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1896","image_path":"images/combination_1896.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1896_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1896_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_1896_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1896_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1896,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1897","image_path":"images/combination_1897.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1897_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1897_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1897_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1897_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1897_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1897,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[569,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1898","image_path":"images/combination_1898.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1898_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1898_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1898_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":"combination_1898_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1898_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1898,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[559,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1899","image_path":"images/combination_1899.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1899_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1899_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1899_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":"combination_1899_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1899_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1899,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1900","image_path":"images/combination_1900.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1900_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1900_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1900_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":"combination_1900_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1900_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1900,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1901","image_path":"images/combination_1901.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1901_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1901_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1901_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":"combination_1901_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1901_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1901,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,3],[1,4],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1902","image_path":"images/combination_1902.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1902_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1902_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1902_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":"combination_1902_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1902_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1902,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,3],[1,4],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[594,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1903","image_path":"images/combination_1903.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1903_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1903_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1903_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":"combination_1903_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1903_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1903,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7}],"canvas_size":[580,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1904","image_path":"images/combination_1904.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1904_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1904_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1904_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1904_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1904_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1904,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":5}],"canvas_size":[556,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1905","image_path":"images/combination_1905.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1905_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1905_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1905_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1905_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1905_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1905,"target_cell_count":6,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[563,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1906","image_path":"images/combination_1906.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1906_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1906_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1906_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1906_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1906_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1906,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[1,5],[2,5]]],"total_cell_count":10}],"canvas_size":[565,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1907","image_path":"images/combination_1907.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1907_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1907_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1907_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":"combination_1907_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1907_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1907,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[563,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1908","image_path":"images/combination_1908.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1908_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1908_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1908_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":"combination_1908_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1908_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1908,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[567,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1909","image_path":"images/combination_1909.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1909_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1909_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1909_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":"combination_1909_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1909_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1909,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1910","image_path":"images/combination_1910.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1910_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1910_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1910_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1910_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1910_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1910,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[572,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1911","image_path":"images/combination_1911.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1911_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1911_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1911_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":"combination_1911_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1911_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1911,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1912","image_path":"images/combination_1912.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1912_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1912_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1912_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1912_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1912_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1912,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[582,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1913","image_path":"images/combination_1913.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1913_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1913_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1913_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1913_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1913_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1913,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]]],"total_cell_count":8}],"canvas_size":[550,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1914","image_path":"images/combination_1914.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1914_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1914_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1914_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1914_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1914_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1914,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,403],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1915","image_path":"images/combination_1915.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1915_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1915_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1915_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1915_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1915_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1915,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1916","image_path":"images/combination_1916.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1916_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1916_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1916_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1916_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1916_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1916,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[564,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1917","image_path":"images/combination_1917.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1917_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1917_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1917_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":"combination_1917_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1917_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1917,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[554,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1918","image_path":"images/combination_1918.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1918_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1918_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1918_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1918_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1918_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1918,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[571,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1919","image_path":"images/combination_1919.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1919_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1919_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1919_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1919_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1919,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[581,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1920","image_path":"images/combination_1920.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1920_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1920_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1920_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":"combination_1920_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1920_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1920,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[589,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1921","image_path":"images/combination_1921.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1921_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1921_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1921_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":"combination_1921_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1921_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1921,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1922","image_path":"images/combination_1922.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1922_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1922_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1922_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1922_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1922_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1922,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[581,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_1923","image_path":"images/combination_1923.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1923_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1923_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1923_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1923_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1923_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1923,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[568,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1924","image_path":"images/combination_1924.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1924_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1924_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1924_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":"combination_1924_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1924_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1924,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[559,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1925","image_path":"images/combination_1925.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1925_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1925_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_1925_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1925_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1925,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[598,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1926","image_path":"images/combination_1926.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1926_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1926_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1926_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":"combination_1926_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1926_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1926,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1927","image_path":"images/combination_1927.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1927_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1927_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1927_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":"combination_1927_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1927_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1927,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3],[4,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1928","image_path":"images/combination_1928.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1928_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1928_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1928_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1928_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1928_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1928,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,2],[3,3],[4,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[4,0],[4,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2],[3,3],[4,2]]],"total_cell_count":9}],"canvas_size":[599,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1929","image_path":"images/combination_1929.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1929_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1929_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1929_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":"combination_1929_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1929_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1929,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2],[4,2],[4,3],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[599,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1930","image_path":"images/combination_1930.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1930_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1930_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1930_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1930_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1930_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1930,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1931","image_path":"images/combination_1931.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1931_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1931_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1931_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":"combination_1931_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1931_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1931,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[571,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1932","image_path":"images/combination_1932.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1932_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1932_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1932_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":"combination_1932_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1932_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1932,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[570,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1933","image_path":"images/combination_1933.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1933_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1933_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1933_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1933_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1933_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1933,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[567,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1934","image_path":"images/combination_1934.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1934_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1934_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1934_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1934_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1934_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1934,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[559,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1935","image_path":"images/combination_1935.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1935_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1935_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_1935_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":"combination_1935_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1935_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1935,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[2,3],[2,4],[3,0],[3,1],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10}],"canvas_size":[573,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1936","image_path":"images/combination_1936.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1936_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1936_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1936_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1936_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1936_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1936,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":9}],"canvas_size":[587,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1937","image_path":"images/combination_1937.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1937_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1937_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_1937_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1937_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1937,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[583,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1938","image_path":"images/combination_1938.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1938_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1938_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1938_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1938_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1938_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1938,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_1939","image_path":"images/combination_1939.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1939_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1939_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1939_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":"combination_1939_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1939_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1939,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1940","image_path":"images/combination_1940.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1940_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1940_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1940_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1940_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1940_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1940,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[581,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1941","image_path":"images/combination_1941.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1941_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1941_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1941_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":"combination_1941_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1941_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1941,"target_cell_count":6,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[568,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1942","image_path":"images/combination_1942.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1942_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1942_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_1942_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":"combination_1942_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1942_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1942,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[594,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1943","image_path":"images/combination_1943.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1943_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1943_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1943_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1943_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1943_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1943,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[553,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1944","image_path":"images/combination_1944.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1944_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1944_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1944_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1944_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1944_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1944,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[576,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1945","image_path":"images/combination_1945.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1945_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1945_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1945_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":"combination_1945_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1945_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1945,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[563,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1946","image_path":"images/combination_1946.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1946_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1946_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1946_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":"combination_1946_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1946_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1946,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1947","image_path":"images/combination_1947.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1947_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1947_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"A","question_id":"combination_1947_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1947_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1947,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[576,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1948","image_path":"images/combination_1948.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1948_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1948_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1948_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":"combination_1948_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1948_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1948,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5}],"canvas_size":[585,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1949","image_path":"images/combination_1949.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1949_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1949_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1949_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1949_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1949_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1949,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[565,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1950","image_path":"images/combination_1950.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1950_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1950_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1950_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":"combination_1950_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1950_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1950,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[558,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1951","image_path":"images/combination_1951.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1951_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1951_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_1951_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":"combination_1951_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1951_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1951,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1952","image_path":"images/combination_1952.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1952_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1952_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1952_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1952_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1952_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1952,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1953","image_path":"images/combination_1953.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1953_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1953_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1953_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1953_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1953_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1953,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1954","image_path":"images/combination_1954.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1954_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1954_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1954_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1954_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1954_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1954,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[597,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1955","image_path":"images/combination_1955.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1955_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1955_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1955_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1955_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1955_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1955,"target_cell_count":7,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[595,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1956","image_path":"images/combination_1956.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1956_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1956_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1956_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1956_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1956_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1956,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[581,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1957","image_path":"images/combination_1957.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1957_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1957_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1957_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1957_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1957_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1957,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[592,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1958","image_path":"images/combination_1958.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1958_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1958_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1958_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":"combination_1958_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1958_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1958,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":5}],"canvas_size":[592,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1959","image_path":"images/combination_1959.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1959_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1959_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1959_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1959_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1959_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1959,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[567,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1960","image_path":"images/combination_1960.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1960_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1960_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_1960_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":"combination_1960_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1960_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1960,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[592,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1961","image_path":"images/combination_1961.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1961_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1961_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1961_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":"combination_1961_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1961_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1961,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1962","image_path":"images/combination_1962.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1962_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1962_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1962_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1962_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1962_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1962,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1963","image_path":"images/combination_1963.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1963_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1963_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1963_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":"combination_1963_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1963_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1963,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[590,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1964","image_path":"images/combination_1964.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1964_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1964_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1964_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":"combination_1964_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1964_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1964,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[590,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1965","image_path":"images/combination_1965.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1965_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1965_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1965_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":"combination_1965_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1965_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1965,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[599,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_1966","image_path":"images/combination_1966.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1966_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1966_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1966_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1966_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1966_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1966,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[4,0],[5,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[586,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1967","image_path":"images/combination_1967.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1967_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1967_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1967_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":"combination_1967_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1967_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1967,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1968","image_path":"images/combination_1968.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1968_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1968_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1968_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":"combination_1968_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1968_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1968,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[575,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1969","image_path":"images/combination_1969.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1969_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1969_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1969_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1969_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1969_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1969,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[558,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1970","image_path":"images/combination_1970.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1970_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1970_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1970_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1970_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1970_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1970,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[562,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1971","image_path":"images/combination_1971.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1971_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1971_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_1971_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":"combination_1971_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1971_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1971,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[590,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1972","image_path":"images/combination_1972.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1972_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1972_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1972_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":"combination_1972_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1972_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1972,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[561,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1973","image_path":"images/combination_1973.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1973_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1973_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_1973_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1973_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1973_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1973,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[550,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1974","image_path":"images/combination_1974.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1974_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1974_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1974_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":"combination_1974_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1974_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1974,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[590,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1975","image_path":"images/combination_1975.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1975_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1975_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_1975_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":"combination_1975_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1975_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1975,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[550,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1976","image_path":"images/combination_1976.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1976_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1976_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1976_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1976_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1976_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1976,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":9}],"canvas_size":[579,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1977","image_path":"images/combination_1977.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1977_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1977_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1977_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":"combination_1977_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1977_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1977,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1978","image_path":"images/combination_1978.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1978_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1978_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_1978_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":"combination_1978_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1978_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1978,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7}],"canvas_size":[555,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1979","image_path":"images/combination_1979.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1979_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1979_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1979_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1979_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1979_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1979,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3],[2,4]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_1980","image_path":"images/combination_1980.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1980_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1980_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1980_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1980_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_1980_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1980,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]]],"total_cell_count":10}],"canvas_size":[561,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1981","image_path":"images/combination_1981.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1981_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1981_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_1981_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1981_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1981_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1981,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_1982","image_path":"images/combination_1982.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1982_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1982_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1982_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1982_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1982_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1982,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[597,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1983","image_path":"images/combination_1983.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1983_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1983_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1983_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1983_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1983_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1983,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[573,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1984","image_path":"images/combination_1984.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1984_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1984_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_1984_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":"combination_1984_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1984_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1984,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1985","image_path":"images/combination_1985.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1985_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1985_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_1985_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1985_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1985_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1985,"target_cell_count":8,"target_cells":[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1986","image_path":"images/combination_1986.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1986_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1986_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1986_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1986_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1986_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1986,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3],[2,4]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[580,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_1987","image_path":"images/combination_1987.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1987_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1987_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1987_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1987_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1987_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1987,"target_cell_count":10,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[585,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_1988","image_path":"images/combination_1988.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_1988_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1988_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1988_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":"combination_1988_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1988_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1988,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1989","image_path":"images/combination_1989.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1989_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1989_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1989_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1989_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1989_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1989,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[550,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1990","image_path":"images/combination_1990.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1990_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1990_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_1990_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":"combination_1990_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1990_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1990,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1991","image_path":"images/combination_1991.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1991_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1991_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_1991_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":"combination_1991_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1991_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1991,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_1992","image_path":"images/combination_1992.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1992_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1992_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_1992_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":"combination_1992_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1992_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1992,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[580,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1993","image_path":"images/combination_1993.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1993_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1993_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1993_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1993_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1993_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1993,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]],"total_cell_count":8}],"canvas_size":[580,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_1994","image_path":"images/combination_1994.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_1994_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1994_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_1994_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":"combination_1994_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1994_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1994,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1995","image_path":"images/combination_1995.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1995_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1995_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_1995_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1995_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1995,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[586,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_1996","image_path":"images/combination_1996.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_1996_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_1996_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_1996_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_1996_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1996_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1996,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[599,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_1997","image_path":"images/combination_1997.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_1997_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_1997_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1997_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_1997_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1997_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1997,"target_cell_count":6,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_1998","image_path":"images/combination_1998.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1998_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_1998_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1998_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_1998_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_1998_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":1998,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[557,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_1999","image_path":"images/combination_1999.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_1999_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_1999_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_1999_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_1999_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_1999_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":1999,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2000","image_path":"images/combination_2000.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2000_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2000_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2000_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2000_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2000_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2000,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[587,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2001","image_path":"images/combination_2001.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2001_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2001_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2001_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":"combination_2001_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2001_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2001,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[4,0],[4,1],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[4,0],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[3,0],[3,1],[4,0],[5,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[596,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2002","image_path":"images/combination_2002.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2002_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2002_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2002_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":"combination_2002_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2002_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2002,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[557,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2003","image_path":"images/combination_2003.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2003_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2003_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2003_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":"combination_2003_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2003_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2003,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[583,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2004","image_path":"images/combination_2004.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2004_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2004_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2004_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2004_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2004_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2004,"target_cell_count":10,"target_cells":[[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[578,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2005","image_path":"images/combination_2005.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2005_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2005_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2005_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2005_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2005_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2005,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[585,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2006","image_path":"images/combination_2006.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2006_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2006_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2006_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":"combination_2006_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2006_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2006,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[562,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2007","image_path":"images/combination_2007.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2007_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2007_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2007_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2007_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2007_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2007,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[559,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2008","image_path":"images/combination_2008.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2008_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2008_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2008_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2008_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2008_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2008,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[567,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2009","image_path":"images/combination_2009.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2009_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2009_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2009_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2009_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2009_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2009,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9}],"canvas_size":[558,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2010","image_path":"images/combination_2010.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2010_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2010_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2010_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2010_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2010_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2010,"target_cell_count":9,"target_cells":[[0,4],[1,1],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[583,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2011","image_path":"images/combination_2011.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2011_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2011_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2011_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2011_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2011_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2011,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[556,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2012","image_path":"images/combination_2012.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2012_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2012_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2012_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":"combination_2012_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2012_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2012,"target_cell_count":8,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8}],"canvas_size":[577,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2013","image_path":"images/combination_2013.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2013_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2013_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2013_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":"combination_2013_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2013_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2013,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2014","image_path":"images/combination_2014.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2014_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2014_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2014_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":"combination_2014_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2014_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2014,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2015","image_path":"images/combination_2015.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2015_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2015_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2015_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2015_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2015_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2015,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2016","image_path":"images/combination_2016.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2016_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2016_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2016_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":"combination_2016_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2016_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2016,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[562,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2017","image_path":"images/combination_2017.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2017_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2017_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2017_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2017_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2017_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2017,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[584,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2018","image_path":"images/combination_2018.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2018_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2018_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2018_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2018_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2018_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2018,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[559,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2019","image_path":"images/combination_2019.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2019_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2019_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2019_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2019_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2019_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2019,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2020","image_path":"images/combination_2020.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2020_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2020_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2020_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2020_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2020_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2020,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[575,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2021","image_path":"images/combination_2021.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2021_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2021_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2021_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":"combination_2021_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2021_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2021,"target_cell_count":10,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[584,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2022","image_path":"images/combination_2022.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2022_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2022_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2022_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":"combination_2022_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2022_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2022,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[574,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2023","image_path":"images/combination_2023.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2023_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2023_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2023_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2023_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2023_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2023,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[580,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2024","image_path":"images/combination_2024.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2024_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2024_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2024_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":"combination_2024_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2024_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2024,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2025","image_path":"images/combination_2025.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2025_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2025_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2025_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":"combination_2025_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2025_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2025,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[557,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2026","image_path":"images/combination_2026.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2026_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2026_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2026_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2026_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2026_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2026,"target_cell_count":10,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[556,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2027","image_path":"images/combination_2027.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2027_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2027_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2027_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2027_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2027_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2027,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[572,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2028","image_path":"images/combination_2028.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2028_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2028_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2028_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2028_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2028_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2028,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9}],"canvas_size":[596,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2029","image_path":"images/combination_2029.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2029_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2029_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_2029_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2029_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2029,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[568,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2030","image_path":"images/combination_2030.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2030_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2030_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2030_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":"combination_2030_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2030_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2030,"target_cell_count":8,"target_cells":[[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[592,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2031","image_path":"images/combination_2031.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2031_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2031_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2031_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2031_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2031_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2031,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[552,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2032","image_path":"images/combination_2032.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2032_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2032_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2032_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2032_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2032_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2032,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":5}],"canvas_size":[576,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2033","image_path":"images/combination_2033.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2033_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2033_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2033_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2033_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2033_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2033,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[554,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2034","image_path":"images/combination_2034.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2034_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2034_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2034_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":"combination_2034_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2034_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2034,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[569,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2035","image_path":"images/combination_2035.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2035_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2035_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_2035_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2035_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2035,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2036","image_path":"images/combination_2036.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2036_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2036_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2036_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":"combination_2036_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2036_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2036,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[566,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2037","image_path":"images/combination_2037.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2037_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2037_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2037_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":"combination_2037_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2037_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2037,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[555,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2038","image_path":"images/combination_2038.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2038_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2038_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2038_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2038_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2038_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2038,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1],[4,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[592,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2039","image_path":"images/combination_2039.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2039_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2039_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2039_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":"combination_2039_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2039_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2039,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2040","image_path":"images/combination_2040.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2040_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2040_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2040_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":"combination_2040_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2040_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2040,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[552,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2041","image_path":"images/combination_2041.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2041_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2041_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2041_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2041_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2041_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2041,"target_cell_count":10,"target_cells":[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[599,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2042","image_path":"images/combination_2042.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2042_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2042_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2042_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2042_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2042_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2042,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[580,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2043","image_path":"images/combination_2043.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2043_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2043_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2043_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":"combination_2043_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2043_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2043,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2044","image_path":"images/combination_2044.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2044_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2044_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2044_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":"combination_2044_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2044_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2044,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":5}],"canvas_size":[558,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2045","image_path":"images/combination_2045.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2045_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2045_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2045_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":"combination_2045_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2045_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2045,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":7}],"canvas_size":[585,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2046","image_path":"images/combination_2046.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2046_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2046_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2046_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2046_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2046_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2046,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[590,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2047","image_path":"images/combination_2047.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2047_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2047_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2047_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":"combination_2047_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2047_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2047,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2],[3,2]]],"total_cell_count":10}],"canvas_size":[568,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2048","image_path":"images/combination_2048.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2048_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2048_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2048_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":"combination_2048_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2048_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2048,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[583,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2049","image_path":"images/combination_2049.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2049_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2049_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2049_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2049_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2049_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2049,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[587,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2050","image_path":"images/combination_2050.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2050_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2050_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2050_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2050_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2050_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2050,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[563,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2051","image_path":"images/combination_2051.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2051_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2051_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2051_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":"combination_2051_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2051_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2051,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[592,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2052","image_path":"images/combination_2052.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2052_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2052_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2052_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":"combination_2052_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2052_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2052,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[568,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2053","image_path":"images/combination_2053.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2053_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2053_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2053_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2053_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2053_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2053,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":5}],"canvas_size":[563,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2054","image_path":"images/combination_2054.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2054_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2054_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2054_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2054_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2054_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2054,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2055","image_path":"images/combination_2055.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2055_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2055_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2055_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":"combination_2055_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2055_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2055,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[582,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2056","image_path":"images/combination_2056.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2056_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2056_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2056_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2056_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2056_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2056,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[595,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2057","image_path":"images/combination_2057.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2057_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2057_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2057_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2057_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2057_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2057,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[559,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2058","image_path":"images/combination_2058.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2058_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2058_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2058_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2058_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2058_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2058,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[576,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2059","image_path":"images/combination_2059.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2059_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2059_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_2059_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2059_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2059,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[586,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2060","image_path":"images/combination_2060.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2060_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2060_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2060_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":"combination_2060_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2060_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2060,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[5,0]]],"total_cell_count":8}],"canvas_size":[573,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2061","image_path":"images/combination_2061.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2061_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2061_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2061_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2061_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2061_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2061,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[571,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2062","image_path":"images/combination_2062.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2062_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2062_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2062_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":"combination_2062_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2062_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2062,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[559,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2063","image_path":"images/combination_2063.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2063_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2063_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2063_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":"combination_2063_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2063_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2063,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[595,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2064","image_path":"images/combination_2064.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2064_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2064_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2064_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":"combination_2064_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2064_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2064,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2065","image_path":"images/combination_2065.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2065_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2065_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2065_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2065_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2065_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2065,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2066","image_path":"images/combination_2066.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2066_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2066_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2066_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2066_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2066_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2066,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[555,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2067","image_path":"images/combination_2067.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2067_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2067_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2067_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":"combination_2067_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2067_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2067,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6}],"canvas_size":[599,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2068","image_path":"images/combination_2068.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2068_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2068_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2068_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2068_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2068_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2068,"target_cell_count":6,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[573,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2069","image_path":"images/combination_2069.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2069_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2069_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2069_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":"combination_2069_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2069_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2069,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[574,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2070","image_path":"images/combination_2070.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2070_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2070_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2070_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2070_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2070_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2070,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[550,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2071","image_path":"images/combination_2071.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2071_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2071_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2071_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":"combination_2071_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2071_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2071,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[572,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2072","image_path":"images/combination_2072.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2072_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2072_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2072_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2072_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2072_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2072,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[562,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2073","image_path":"images/combination_2073.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2073_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2073_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2073_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":"combination_2073_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2073_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2073,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7}],"canvas_size":[591,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2074","image_path":"images/combination_2074.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2074_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2074_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2074_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2074_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2074_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2074,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1],[4,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[588,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2075","image_path":"images/combination_2075.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2075_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2075_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2075_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2075_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2075_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2075,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[562,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2076","image_path":"images/combination_2076.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2076_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2076_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2076_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":"combination_2076_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2076_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2076,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[572,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2077","image_path":"images/combination_2077.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2077_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2077_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2077_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2077_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2077_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2077,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":5}],"canvas_size":[552,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2078","image_path":"images/combination_2078.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2078_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2078_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2078_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2078_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2078_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2078,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[579,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2079","image_path":"images/combination_2079.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2079_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2079_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2079_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":"combination_2079_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2079_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2079,"target_cell_count":7,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[552,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2080","image_path":"images/combination_2080.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2080_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2080_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2080_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":"combination_2080_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2080_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2080,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[580,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2081","image_path":"images/combination_2081.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2081_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2081_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2081_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":"combination_2081_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2081_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2081,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[597,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2082","image_path":"images/combination_2082.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2082_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2082_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2082_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2082_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2082_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2082,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[551,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2083","image_path":"images/combination_2083.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2083_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2083_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2083_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":"combination_2083_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2083_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2083,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]],"total_cell_count":10}],"canvas_size":[577,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2084","image_path":"images/combination_2084.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2084_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2084_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2084_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":"combination_2084_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2084_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2084,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2085","image_path":"images/combination_2085.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2085_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2085_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2085_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":"combination_2085_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2085_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2085,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[590,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2086","image_path":"images/combination_2086.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2086_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2086_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2086_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2086_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2086_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2086,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[558,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2087","image_path":"images/combination_2087.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2087_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2087_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2087_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2087_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2087_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2087,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2088","image_path":"images/combination_2088.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2088_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2088_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2088_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2088_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2088_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2088,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[598,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2089","image_path":"images/combination_2089.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2089_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2089_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2089_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":"combination_2089_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2089_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2089,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2090","image_path":"images/combination_2090.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2090_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2090_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2090_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":"combination_2090_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2090_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2090,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2091","image_path":"images/combination_2091.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2091_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2091_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2091_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":"combination_2091_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2091_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2091,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[600,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2092","image_path":"images/combination_2092.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2092_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2092_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2092_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2092_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2092_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2092,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[0,1],[1,1],[2,1],[3,1]]],"total_cell_count":10}],"canvas_size":[577,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2093","image_path":"images/combination_2093.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2093_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2093_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2093_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":"combination_2093_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2093_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2093,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2094","image_path":"images/combination_2094.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2094_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2094_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2094_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2094_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2094_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2094,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0],[3,0],[3,1],[3,2],[4,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[585,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2095","image_path":"images/combination_2095.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2095_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2095_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2095_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2095_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2095_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2095,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[551,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2096","image_path":"images/combination_2096.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2096_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2096_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2096_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2096_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2096_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2096,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_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],[0,2],[0,3],[1,3]]],"total_cell_count":9}],"canvas_size":[555,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2097","image_path":"images/combination_2097.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2097_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2097_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2097_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2097_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2097_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2097,"target_cell_count":9,"target_cells":[[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[565,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2098","image_path":"images/combination_2098.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2098_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2098_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2098_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2098_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2098_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2098,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[3,3],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[577,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2099","image_path":"images/combination_2099.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2099_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2099_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2099_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":"combination_2099_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2099_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2099,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[598,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2100","image_path":"images/combination_2100.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2100_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2100_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2100_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2100_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2100_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2100,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[596,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2101","image_path":"images/combination_2101.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2101_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2101_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2101_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2101_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2101_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2101,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2102","image_path":"images/combination_2102.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2102_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2102_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_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":"combination_2102_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2102_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2102,"target_cell_count":10,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[599,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2103","image_path":"images/combination_2103.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2103_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2103_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2103_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":"combination_2103_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2103_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2103,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[561,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2104","image_path":"images/combination_2104.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2104_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2104_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2104_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":"combination_2104_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2104_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2104,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[559,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2105","image_path":"images/combination_2105.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2105_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2105_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_2105_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2105_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2105,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2106","image_path":"images/combination_2106.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2106_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2106_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2106_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":"combination_2106_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2106_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2106,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[599,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2107","image_path":"images/combination_2107.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2107_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2107_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2107_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2107_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2107_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2107,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[600,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2108","image_path":"images/combination_2108.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2108_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2108_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2108_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2108_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2108_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2108,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4],[1,1],[1,2],[1,3],[1,4],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3],[2,4],[3,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[575,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2109","image_path":"images/combination_2109.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2109_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2109_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_2109_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2109_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2109,"target_cell_count":9,"target_cells":[[0,4],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2110","image_path":"images/combination_2110.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2110_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2110_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2110_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2110_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2110_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2110,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2111","image_path":"images/combination_2111.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2111_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2111_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2111_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":"combination_2111_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2111_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2111,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2112","image_path":"images/combination_2112.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2112_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2112_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_2112_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2112_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2112,"target_cell_count":8,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":8}],"canvas_size":[550,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2113","image_path":"images/combination_2113.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2113_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2113_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2113_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2113_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2113_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2113,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[565,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2114","image_path":"images/combination_2114.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2114_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2114_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2114_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2114_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2114_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2114,"target_cell_count":9,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[572,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2115","image_path":"images/combination_2115.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2115_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2115_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2115_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2115_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2115_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2115,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[586,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2116","image_path":"images/combination_2116.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2116_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2116_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2116_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2116_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2116_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2116,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2117","image_path":"images/combination_2117.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2117_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2117_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2117_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2117_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2117_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2117,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[577,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2118","image_path":"images/combination_2118.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2118_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2118_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2118_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2118_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2118_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2118,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[561,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2119","image_path":"images/combination_2119.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2119_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2119_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2119_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2119_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2119_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2119,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2120","image_path":"images/combination_2120.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2120_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2120_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2120_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":"combination_2120_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2120_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2120,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[561,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2121","image_path":"images/combination_2121.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2121_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2121_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2121_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2121_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2121_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2121,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[575,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2122","image_path":"images/combination_2122.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2122_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2122_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2122_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2122_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2122_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2122,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0],[5,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[5,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[595,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2123","image_path":"images/combination_2123.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2123_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2123_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2123_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2123_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2123_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2123,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[550,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2124","image_path":"images/combination_2124.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2124_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2124_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2124_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":"combination_2124_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2124_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2124,"target_cell_count":7,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,4]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2125","image_path":"images/combination_2125.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2125_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2125_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2125_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2125_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2125_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2125,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2],[3,3],[3,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":9}],"canvas_size":[565,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2126","image_path":"images/combination_2126.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2126_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2126_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2126_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2126_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2126_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2126,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[557,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2127","image_path":"images/combination_2127.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2127_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2127_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2127_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":"combination_2127_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2127_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2127,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[557,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2128","image_path":"images/combination_2128.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2128_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2128_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2128_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":"combination_2128_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2128_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2128,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":8}],"canvas_size":[559,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2129","image_path":"images/combination_2129.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2129_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2129_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2129_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":"combination_2129_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2129_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2129,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[564,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2130","image_path":"images/combination_2130.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2130_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2130_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2130_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2130_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2130_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2130,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2131","image_path":"images/combination_2131.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2131_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2131_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2131_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2131_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2131_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2131,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[578,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2132","image_path":"images/combination_2132.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2132_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2132_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2132_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2132_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2132_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2132,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2133","image_path":"images/combination_2133.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2133_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2133_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2133_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":"combination_2133_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2133_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2133,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[579,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2134","image_path":"images/combination_2134.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2134_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2134_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2134_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2134_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2134_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2134,"target_cell_count":10,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[588,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2135","image_path":"images/combination_2135.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2135_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2135_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2135_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":"combination_2135_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2135_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2135,"target_cell_count":7,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[560,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2136","image_path":"images/combination_2136.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2136_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2136_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2136_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":"combination_2136_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2136_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2136,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[586,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2137","image_path":"images/combination_2137.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2137_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2137_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2137_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2137_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2137_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2137,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8}],"canvas_size":[586,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2138","image_path":"images/combination_2138.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2138_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2138_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2138_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":"combination_2138_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2138_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2138,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2139","image_path":"images/combination_2139.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2139_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2139_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2139_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":"combination_2139_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2139_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2139,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[586,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2140","image_path":"images/combination_2140.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2140_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2140_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2140_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2140_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2140_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2140,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2141","image_path":"images/combination_2141.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2141_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2141_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2141_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":"combination_2141_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2141_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2141,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[593,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2142","image_path":"images/combination_2142.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2142_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2142_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2142_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2142_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2142_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2142,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[583,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2143","image_path":"images/combination_2143.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2143_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2143_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2143_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2143_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2143_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2143,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[576,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2144","image_path":"images/combination_2144.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2144_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2144_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2144_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2144_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2144_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2144,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,4],[1,2],[1,3],[1,4]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,4]],[[0,0],[1,0]],[[0,0]]],"total_cell_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],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[574,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2145","image_path":"images/combination_2145.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2145_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2145_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2145_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":"combination_2145_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2145_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2145,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[561,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2146","image_path":"images/combination_2146.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2146_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2146_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2146_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2146_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2146_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2146,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[560,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2147","image_path":"images/combination_2147.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2147_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2147_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2147_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2147_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2147_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2147,"target_cell_count":9,"target_cells":[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2148","image_path":"images/combination_2148.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2148_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2148_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2148_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2148_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2148_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2148,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[600,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2149","image_path":"images/combination_2149.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2149_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2149_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2149_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2149_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2149_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2149,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[574,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2150","image_path":"images/combination_2150.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2150_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2150_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2150_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2150_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2150_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2150,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]],"total_cell_count":9}],"canvas_size":[588,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2151","image_path":"images/combination_2151.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2151_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2151_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2151_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":"combination_2151_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2151_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2151,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4],[2,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":8}],"canvas_size":[581,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2152","image_path":"images/combination_2152.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2152_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2152_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2152_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":"combination_2152_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2152_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2152,"target_cell_count":8,"target_cells":[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2153","image_path":"images/combination_2153.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2153_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2153_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2153_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2153_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2153_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2153,"target_cell_count":7,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[595,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2154","image_path":"images/combination_2154.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2154_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2154_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2154_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2154_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2154_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2154,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[551,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2155","image_path":"images/combination_2155.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2155_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2155_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2155_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2155_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2155_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2155,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[590,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2156","image_path":"images/combination_2156.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2156_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2156_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2156_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":"combination_2156_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2156_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2156,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[599,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2157","image_path":"images/combination_2157.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2157_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2157_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2157_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2157_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2157_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2157,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[585,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2158","image_path":"images/combination_2158.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2158_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2158_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2158_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2158_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2158,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[570,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2159","image_path":"images/combination_2159.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2159_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2159_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2159_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2159_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2159_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2159,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,3],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2160","image_path":"images/combination_2160.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2160_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2160_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2160_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":"combination_2160_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2160_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2160,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[594,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2161","image_path":"images/combination_2161.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2161_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2161_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2161_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":"combination_2161_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2161_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2161,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2162","image_path":"images/combination_2162.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2162_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2162_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2162_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2162_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2162_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2162,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[583,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2163","image_path":"images/combination_2163.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2163_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2163_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2163_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":"combination_2163_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2163_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2163,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[569,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2164","image_path":"images/combination_2164.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2164_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2164_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2164_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2164_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2164_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2164,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":9}],"canvas_size":[581,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2165","image_path":"images/combination_2165.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2165_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2165_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_2165_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":"combination_2165_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2165_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2165,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[558,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2166","image_path":"images/combination_2166.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2166_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2166_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2166_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2166_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2166_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2166,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2167","image_path":"images/combination_2167.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2167_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2167_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_2167_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":"combination_2167_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2167_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2167,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[556,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2168","image_path":"images/combination_2168.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2168_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2168_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2168_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":"combination_2168_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2168_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2168,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[571,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2169","image_path":"images/combination_2169.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2169_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2169_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2169_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2169_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2169_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2169,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[577,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2170","image_path":"images/combination_2170.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2170_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2170_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2170_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2170_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2170_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2170,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[565,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2171","image_path":"images/combination_2171.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2171_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2171_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2171_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2171_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2171_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2171,"target_cell_count":10,"target_cells":[[0,3],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[583,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2172","image_path":"images/combination_2172.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2172_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2172_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2172_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2172_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2172_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2172,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[593,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2173","image_path":"images/combination_2173.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2173_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2173_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2173_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2173_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2173_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2173,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[553,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2174","image_path":"images/combination_2174.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2174_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2174_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2174_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":"combination_2174_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2174_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2174,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9}],"canvas_size":[573,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2175","image_path":"images/combination_2175.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2175_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2175_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2175_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2175_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2175_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2175,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2176","image_path":"images/combination_2176.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2176_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2176_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2176_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":"combination_2176_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2176_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2176,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2177","image_path":"images/combination_2177.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2177_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2177_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2177_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":"combination_2177_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2177_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2177,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[3,3],[3,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[595,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2178","image_path":"images/combination_2178.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2178_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2178_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2178_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":"combination_2178_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2178_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2178,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[3,3],[3,4],[4,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[572,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2179","image_path":"images/combination_2179.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2179_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2179_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2179_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":"combination_2179_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2179_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2179,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,3],[1,4],[1,5]],[[0,0]]],"total_cell_count":10}],"canvas_size":[560,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2180","image_path":"images/combination_2180.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2180_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2180_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2180_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":"combination_2180_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2180_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2180,"target_cell_count":10,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[559,434],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2181","image_path":"images/combination_2181.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2181_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2181_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2181_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2181_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2181_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2181,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2182","image_path":"images/combination_2182.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2182_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2182_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2182_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2182_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2182_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2182,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5}],"canvas_size":[582,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2183","image_path":"images/combination_2183.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2183_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2183_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2183_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2183_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2183_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2183,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[552,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2184","image_path":"images/combination_2184.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2184_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2184_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2184_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":"combination_2184_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2184_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2184,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[567,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2185","image_path":"images/combination_2185.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2185_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2185_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2185_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":"combination_2185_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2185_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2185,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[556,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2186","image_path":"images/combination_2186.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2186_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2186_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2186_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2186_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2186_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2186,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[557,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2187","image_path":"images/combination_2187.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2187_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2187_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2187_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2187_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2187_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2187,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[600,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2188","image_path":"images/combination_2188.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2188_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2188_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2188_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2188_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2188_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2188,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2189","image_path":"images/combination_2189.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2189_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2189_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2189_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2189_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2189_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2189,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2190","image_path":"images/combination_2190.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2190_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2190_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2190_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":"combination_2190_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2190_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2190,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]]],"total_cell_count":7},{"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],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[1,4]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8}],"canvas_size":[560,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2191","image_path":"images/combination_2191.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2191_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2191_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2191_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":"combination_2191_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2191_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2191,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[598,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2192","image_path":"images/combination_2192.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2192_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2192_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2192_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2192_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2192_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2192,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[583,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2193","image_path":"images/combination_2193.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2193_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2193_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2193_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2193_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2193_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2193,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2194","image_path":"images/combination_2194.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2194_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2194_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2194_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":"combination_2194_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2194_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2194,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[592,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2195","image_path":"images/combination_2195.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2195_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2195_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2195_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2195_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2195_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2195,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2196","image_path":"images/combination_2196.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2196_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2196_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2196_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2196_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2196_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2196,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":5}],"canvas_size":[591,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2197","image_path":"images/combination_2197.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2197_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2197_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2197_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2197_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2197_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2197,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2198","image_path":"images/combination_2198.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2198_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2198_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2198_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2198_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2198_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2198,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[597,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2199","image_path":"images/combination_2199.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2199_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2199_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2199_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":"combination_2199_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2199_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2199,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[571,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2200","image_path":"images/combination_2200.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2200_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2200_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2200_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":"combination_2200_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2200_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2200,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[598,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2201","image_path":"images/combination_2201.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2201_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2201_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2201_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":"combination_2201_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2201_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2201,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5}],"canvas_size":[551,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2202","image_path":"images/combination_2202.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2202_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2202_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2202_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2202_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2202_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2202,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[584,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2203","image_path":"images/combination_2203.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2203_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2203_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2203_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2203_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2203_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2203,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[553,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2204","image_path":"images/combination_2204.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2204_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2204_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2204_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":"combination_2204_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2204_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2204,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_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],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[586,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2205","image_path":"images/combination_2205.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2205_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2205_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"D","question_id":"combination_2205_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2205_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2205,"target_cell_count":10,"target_cells":[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[578,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2206","image_path":"images/combination_2206.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2206_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2206_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2206_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":"combination_2206_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2206_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2206,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[595,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2207","image_path":"images/combination_2207.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2207_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2207_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2207_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":"combination_2207_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2207_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2207,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[557,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2208","image_path":"images/combination_2208.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2208_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2208_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2208_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":"combination_2208_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2208_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2208,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"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],[0,2],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[554,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2209","image_path":"images/combination_2209.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2209_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2209_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2209_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":"combination_2209_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2209_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2209,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8}],"canvas_size":[596,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2210","image_path":"images/combination_2210.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2210_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2210_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2210_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2210_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2210_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2210,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[582,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2211","image_path":"images/combination_2211.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2211_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2211_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2211_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":"combination_2211_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2211_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2211,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[582,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2212","image_path":"images/combination_2212.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2212_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2212_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2212_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":"combination_2212_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2212_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2212,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[3,0]]],"total_cell_count":9}],"canvas_size":[569,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2213","image_path":"images/combination_2213.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2213_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2213_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2213_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":"combination_2213_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2213_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2213,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,4],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2214","image_path":"images/combination_2214.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2214_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2214_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2214_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2214_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2214_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2214,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,4],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[564,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2215","image_path":"images/combination_2215.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2215_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2215_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2215_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2215_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2215_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2215,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[587,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2216","image_path":"images/combination_2216.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2216_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2216_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2216_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2216_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2216_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2216,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[561,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2217","image_path":"images/combination_2217.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2217_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2217_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2217_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":"combination_2217_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2217_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2217,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[555,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2218","image_path":"images/combination_2218.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2218_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2218_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2218_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":"combination_2218_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2218_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2218,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[592,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2219","image_path":"images/combination_2219.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2219_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2219_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2219_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":"combination_2219_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2219_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2219,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2220","image_path":"images/combination_2220.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2220_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2220_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2220_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":"combination_2220_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2220_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2220,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[597,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2221","image_path":"images/combination_2221.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2221_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2221_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2221_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2221_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2221_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2221,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[563,417],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2222","image_path":"images/combination_2222.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2222_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2222_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2222_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2222_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2222_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2222,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":7}],"canvas_size":[597,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2223","image_path":"images/combination_2223.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2223_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2223_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2223_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2223_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2223_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2223,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[597,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2224","image_path":"images/combination_2224.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2224_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2224_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2224_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2224_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2224_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2224,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[561,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2225","image_path":"images/combination_2225.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2225_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2225_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2225_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2225_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2225_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2225,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2226","image_path":"images/combination_2226.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2226_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2226_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2226_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":"combination_2226_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2226_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2226,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[596,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2227","image_path":"images/combination_2227.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2227_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2227_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2227_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2227_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2227_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2227,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[568,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2228","image_path":"images/combination_2228.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2228_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2228_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2228_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2228_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2228_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2228,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[578,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2229","image_path":"images/combination_2229.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2229_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2229_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2229_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2229_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2229_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2229,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2230","image_path":"images/combination_2230.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2230_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2230_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2230_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2230_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2230_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2230,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[600,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2231","image_path":"images/combination_2231.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2231_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2231_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2231_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":"combination_2231_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2231_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2231,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[597,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2232","image_path":"images/combination_2232.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2232_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2232_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2232_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2232_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2232_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2232,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":5}],"canvas_size":[582,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2233","image_path":"images/combination_2233.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2233_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2233_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2233_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2233_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2233_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2233,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[600,440],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2234","image_path":"images/combination_2234.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2234_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2234_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2234_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2234_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2234_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2234,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6}],"canvas_size":[566,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2235","image_path":"images/combination_2235.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2235_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2235_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2235_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":"combination_2235_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2235_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2235,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1],[4,2],[5,1],[5,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[585,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2236","image_path":"images/combination_2236.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2236_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2236_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2236_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2236_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2236_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2236,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2],[5,1],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2237","image_path":"images/combination_2237.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2237_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2237_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2237_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2237_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2237_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2237,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[595,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2238","image_path":"images/combination_2238.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2238_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2238_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2238_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2238_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2238_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2238,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[566,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2239","image_path":"images/combination_2239.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2239_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2239_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2239_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2239_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2239_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2239,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[598,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2240","image_path":"images/combination_2240.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2240_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2240_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2240_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2240_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2240_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2240,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[588,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2241","image_path":"images/combination_2241.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2241_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2241_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2241_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":"combination_2241_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2241_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2241,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[582,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2242","image_path":"images/combination_2242.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2242_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2242_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2242_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2242_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2242_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2242,"target_cell_count":8,"target_cells":[[0,4],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2243","image_path":"images/combination_2243.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2243_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2243_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2243_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":"combination_2243_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2243_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2243,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2244","image_path":"images/combination_2244.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2244_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2244_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2244_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":"combination_2244_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2244_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2244,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[558,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2245","image_path":"images/combination_2245.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2245_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2245_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2245_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2245_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2245_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2245,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[592,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2246","image_path":"images/combination_2246.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2246_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2246_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2246_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":"combination_2246_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2246_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2246,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[588,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2247","image_path":"images/combination_2247.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2247_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2247_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2247_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":"combination_2247_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2247_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2247,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6}],"canvas_size":[568,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2248","image_path":"images/combination_2248.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2248_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2248_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2248_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":"combination_2248_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2248_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2248,"target_cell_count":6,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[570,444],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2249","image_path":"images/combination_2249.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2249_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2249_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2249_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":"combination_2249_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2249_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2249,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9}],"canvas_size":[580,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2250","image_path":"images/combination_2250.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2250_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2250_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2250_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2250_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2250_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2250,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2251","image_path":"images/combination_2251.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2251_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2251_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2251_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":"combination_2251_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2251_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2251,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2252","image_path":"images/combination_2252.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2252_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2252_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2252_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":"combination_2252_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2252_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2252,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[579,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2253","image_path":"images/combination_2253.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2253_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2253_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2253_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":"combination_2253_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2253_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2253,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[561,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2254","image_path":"images/combination_2254.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2254_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2254_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2254_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":"combination_2254_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2254_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2254,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[597,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2255","image_path":"images/combination_2255.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2255_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2255_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2255_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":"combination_2255_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2255_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2255,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[557,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2256","image_path":"images/combination_2256.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2256_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2256_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2256_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":"combination_2256_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2256_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2256,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10}],"canvas_size":[552,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2257","image_path":"images/combination_2257.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2257_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2257_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2257_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2257_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2257_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2257,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[554,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2258","image_path":"images/combination_2258.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2258_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2258_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2258_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2258_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2258_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2258,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2259","image_path":"images/combination_2259.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2259_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2259_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2259_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2259_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2259_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2259,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2260","image_path":"images/combination_2260.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2260_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2260_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2260_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":"combination_2260_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2260_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2260,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10}],"canvas_size":[569,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2261","image_path":"images/combination_2261.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2261_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2261_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2261_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2261_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2261_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2261,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[563,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2262","image_path":"images/combination_2262.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2262_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2262_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2262_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":"combination_2262_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2262_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2262,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2263","image_path":"images/combination_2263.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2263_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2263_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2263_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2263_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2263_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2263,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[595,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2264","image_path":"images/combination_2264.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2264_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2264_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2264_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2264_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2264_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2264,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[553,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2265","image_path":"images/combination_2265.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2265_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2265_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2265_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2265_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2265_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2265,"target_cell_count":8,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[599,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2266","image_path":"images/combination_2266.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2266_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2266_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2266_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2266_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2266_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2266,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[584,412],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2267","image_path":"images/combination_2267.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2267_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2267_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2267_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2267_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2267_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2267,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[560,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2268","image_path":"images/combination_2268.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2268_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2268_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2268_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":"combination_2268_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2268_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2268,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[586,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2269","image_path":"images/combination_2269.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2269_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2269_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2269_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2269_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2269_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2269,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[567,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2270","image_path":"images/combination_2270.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2270_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2270_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2270_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2270_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2270_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2270,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[577,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2271","image_path":"images/combination_2271.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2271_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2271_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2271_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2271_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2271_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2271,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2272","image_path":"images/combination_2272.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2272_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2272_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2272_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2272_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2272_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2272,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2273","image_path":"images/combination_2273.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2273_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2273_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2273_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":"combination_2273_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2273_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2273,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":10}],"canvas_size":[595,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2274","image_path":"images/combination_2274.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2274_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2274_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2274_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2274_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2274_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2274,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[587,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2275","image_path":"images/combination_2275.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2275_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2275_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2275_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2275_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2275_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2275,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7}],"canvas_size":[575,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2276","image_path":"images/combination_2276.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2276_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2276_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2276_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":"combination_2276_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2276_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2276,"target_cell_count":7,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[572,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2277","image_path":"images/combination_2277.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2277_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2277_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2277_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":"combination_2277_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2277_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2277,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[559,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2278","image_path":"images/combination_2278.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2278_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2278_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2278_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2278_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2278_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2278,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[578,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2279","image_path":"images/combination_2279.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2279_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2279_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2279_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2279_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2279_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2279,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7}],"canvas_size":[598,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2280","image_path":"images/combination_2280.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2280_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2280_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2280_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2280_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2280_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2280,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[570,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2281","image_path":"images/combination_2281.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2281_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2281_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2281_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2281_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2281_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2281,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2282","image_path":"images/combination_2282.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2282_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2282_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2282_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2282_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2282_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2282,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2283","image_path":"images/combination_2283.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2283_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2283_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2283_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2283_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2283_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2283,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[572,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2284","image_path":"images/combination_2284.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2284_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2284_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2284_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2284_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2284_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2284,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2285","image_path":"images/combination_2285.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2285_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2285_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2285_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2285_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2285_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2285,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[574,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2286","image_path":"images/combination_2286.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2286_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2286_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2286_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":"combination_2286_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2286_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2286,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[592,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2287","image_path":"images/combination_2287.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2287_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2287_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2287_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":"combination_2287_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2287_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2287,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[589,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2288","image_path":"images/combination_2288.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2288_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2288_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2288_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":"combination_2288_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2288_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2288,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[594,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2289","image_path":"images/combination_2289.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2289_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2289_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2289_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":"combination_2289_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2289_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2289,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[591,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2290","image_path":"images/combination_2290.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2290_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2290_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2290_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":"combination_2290_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2290_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2290,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2291","image_path":"images/combination_2291.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2291_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2291_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2291_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2291_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2291_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2291,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[3,3],[4,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0],[4,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0],[4,0]]],"total_cell_count":10}],"canvas_size":[569,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2292","image_path":"images/combination_2292.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2292_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2292_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2292_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2292_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2292_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2292,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[586,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2293","image_path":"images/combination_2293.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2293_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2293_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2293_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2293_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2293_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2293,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[565,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2294","image_path":"images/combination_2294.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2294_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2294_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2294_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2294_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2294_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2294,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9}],"canvas_size":[567,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2295","image_path":"images/combination_2295.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2295_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2295_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2295_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":"combination_2295_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2295_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2295,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2296","image_path":"images/combination_2296.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2296_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2296_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2296_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2296_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2296_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2296,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2297","image_path":"images/combination_2297.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2297_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2297_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2297_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":"combination_2297_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2297_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2297,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[588,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2298","image_path":"images/combination_2298.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2298_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2298_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2298_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":"combination_2298_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2298_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2298,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2299","image_path":"images/combination_2299.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2299_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2299_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2299_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2299_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2299_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2299,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[580,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2300","image_path":"images/combination_2300.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2300_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2300_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2300_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":"combination_2300_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2300_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2300,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[569,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2301","image_path":"images/combination_2301.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2301_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2301_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2301_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":"combination_2301_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2301_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2301,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[554,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2302","image_path":"images/combination_2302.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2302_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2302_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2302_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2302_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2302_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2302,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,403],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2303","image_path":"images/combination_2303.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2303_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2303_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2303_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":"combination_2303_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2303_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2303,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2304","image_path":"images/combination_2304.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2304_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2304_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2304_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2304_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2304_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2304,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[561,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2305","image_path":"images/combination_2305.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2305_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2305_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2305_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2305_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2305_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2305,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[580,406],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2306","image_path":"images/combination_2306.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2306_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2306_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2306_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2306_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2306_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2306,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[568,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2307","image_path":"images/combination_2307.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2307_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2307_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2307_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2307_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2307_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2307,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2308","image_path":"images/combination_2308.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2308_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2308_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2308_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2308_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2308_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2308,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2309","image_path":"images/combination_2309.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2309_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2309_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2309_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2309_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2309_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2309,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2310","image_path":"images/combination_2310.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2310_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2310_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2310_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2310_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2310_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2310,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,1],[1,2],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7}],"canvas_size":[559,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2311","image_path":"images/combination_2311.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2311_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2311_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2311_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2311_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2311_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2311,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0],[5,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1],[5,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[596,445],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2312","image_path":"images/combination_2312.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2312_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2312_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_2312_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2312_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2312,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6}],"canvas_size":[578,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2313","image_path":"images/combination_2313.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2313_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2313_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2313_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2313_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2313_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2313,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[562,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2314","image_path":"images/combination_2314.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2314_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2314_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2314_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2314_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2314_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2314,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[593,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2315","image_path":"images/combination_2315.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2315_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2315_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2315_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2315_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2315_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2315,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":10}],"canvas_size":[592,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2316","image_path":"images/combination_2316.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2316_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2316_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2316_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2316_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2316_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2316,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2317","image_path":"images/combination_2317.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2317_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2317_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2317_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":"combination_2317_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2317_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2317,"target_cell_count":7,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[556,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2318","image_path":"images/combination_2318.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2318_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2318_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2318_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2318_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2318_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2318,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":6}],"canvas_size":[557,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2319","image_path":"images/combination_2319.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2319_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2319_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2319_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2319_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2319_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2319,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[581,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2320","image_path":"images/combination_2320.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2320_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2320_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2320_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2320_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2320_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2320,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[572,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2321","image_path":"images/combination_2321.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2321_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2321_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2321_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2321_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2321_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2321,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[593,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2322","image_path":"images/combination_2322.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2322_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2322_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2322_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2322_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2322_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2322,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[592,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2323","image_path":"images/combination_2323.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2323_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2323_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2323_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2323_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2323_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2323,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]]],"total_cell_count":8}],"canvas_size":[584,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2324","image_path":"images/combination_2324.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2324_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2324_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2324_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2324_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2324_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2324,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[583,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2325","image_path":"images/combination_2325.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2325_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2325_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2325_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2325_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2325_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2325,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2326","image_path":"images/combination_2326.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2326_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2326_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2326_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":"combination_2326_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2326_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2326,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[562,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2327","image_path":"images/combination_2327.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2327_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2327_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2327_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2327_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2327_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2327,"target_cell_count":8,"target_cells":[[0,3],[0,4],[1,3],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2328","image_path":"images/combination_2328.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2328_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2328_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2328_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2328_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2328_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2328,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[4,0],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1],[4,0],[4,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0],[4,1]]],"total_cell_count":8}],"canvas_size":[586,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2329","image_path":"images/combination_2329.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2329_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2329_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2329_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":"combination_2329_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2329_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2329,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[567,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2330","image_path":"images/combination_2330.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2330_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2330_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2330_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2330_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2330_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2330,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[567,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2331","image_path":"images/combination_2331.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2331_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2331_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2331_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2331_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2331_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2331,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_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],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[560,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2332","image_path":"images/combination_2332.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2332_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2332_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2332_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":"combination_2332_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2332_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2332,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2333","image_path":"images/combination_2333.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2333_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2333_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2333_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2333_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2333_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2333,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[588,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2334","image_path":"images/combination_2334.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2334_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2334_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2334_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":"combination_2334_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2334_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2334,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[588,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2335","image_path":"images/combination_2335.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2335_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2335_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2335_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2335_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2335_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2335,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[579,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2336","image_path":"images/combination_2336.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2336_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2336_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2336_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2336_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2336_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2336,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4],[2,5],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[2,4]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[588,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2337","image_path":"images/combination_2337.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2337_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2337_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2337_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":"combination_2337_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2337_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2337,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[583,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2338","image_path":"images/combination_2338.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2338_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2338_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2338_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2338_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2338_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2338,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2339","image_path":"images/combination_2339.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2339_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2339_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2339_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2339_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2339_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2339,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2340","image_path":"images/combination_2340.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2340_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2340_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2340_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2340_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2340_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2340,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[584,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2341","image_path":"images/combination_2341.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2341_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2341_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2341_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2341_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2341_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2341,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[585,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2342","image_path":"images/combination_2342.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2342_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2342_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2342_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2342_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2342_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2342,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[582,403],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2343","image_path":"images/combination_2343.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2343_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2343_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2343_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":"combination_2343_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2343_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2343,"target_cell_count":10,"target_cells":[[0,3],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":8}],"canvas_size":[574,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2344","image_path":"images/combination_2344.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2344_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2344_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2344_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2344_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2344_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2344,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[591,433],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2345","image_path":"images/combination_2345.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2345_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2345_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2345_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2345_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2345_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2345,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2346","image_path":"images/combination_2346.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2346_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2346_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2346_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2346_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2346_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2346,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[563,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2347","image_path":"images/combination_2347.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2347_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2347_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2347_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2347_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2347_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2347,"target_cell_count":8,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[560,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2348","image_path":"images/combination_2348.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2348_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2348_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2348_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":"combination_2348_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2348_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2348,"target_cell_count":7,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[590,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2349","image_path":"images/combination_2349.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2349_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2349_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2349_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2349_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2349_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2349,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2350","image_path":"images/combination_2350.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2350_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2350_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_2350_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":"combination_2350_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2350_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2350,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[580,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2351","image_path":"images/combination_2351.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2351_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2351_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2351_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2351_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2351_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2351,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1],[4,2],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2352","image_path":"images/combination_2352.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2352_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2352_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2352_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":"combination_2352_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2352_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2352,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2353","image_path":"images/combination_2353.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2353_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2353_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2353_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2353_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2353_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2353,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1],[4,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[575,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2354","image_path":"images/combination_2354.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2354_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2354_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2354_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2354_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2354_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2354,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[568,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2355","image_path":"images/combination_2355.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2355_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2355_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2355_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":"combination_2355_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2355_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2355,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2356","image_path":"images/combination_2356.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2356_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2356_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2356_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":"combination_2356_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2356_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2356,"target_cell_count":9,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2357","image_path":"images/combination_2357.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2357_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2357_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2357_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":"combination_2357_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2357_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2357,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[596,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2358","image_path":"images/combination_2358.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2358_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2358_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2358_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2358_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2358_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2358,"target_cell_count":9,"target_cells":[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[585,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2359","image_path":"images/combination_2359.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2359_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2359_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_2359_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2359_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2359,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[579,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2360","image_path":"images/combination_2360.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2360_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2360_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2360_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":"combination_2360_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2360_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2360,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,417],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2361","image_path":"images/combination_2361.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2361_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2361_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2361_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2361_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2361_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2361,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2362","image_path":"images/combination_2362.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2362_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2362_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2362_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2362_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2362_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2362,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]}
{"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],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[583,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2363","image_path":"images/combination_2363.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2363_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2363_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2363_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2363_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2363_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2363,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[568,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2364","image_path":"images/combination_2364.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2364_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2364_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2364_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":"combination_2364_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2364_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2364,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[586,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2365","image_path":"images/combination_2365.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2365_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2365_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2365_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":"combination_2365_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2365_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2365,"target_cell_count":6,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[573,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2366","image_path":"images/combination_2366.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2366_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2366_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2366_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":"combination_2366_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2366_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2366,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[574,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2367","image_path":"images/combination_2367.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2367_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2367_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2367_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2367_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2367_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2367,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2368","image_path":"images/combination_2368.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2368_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2368_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2368_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2368_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2368_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2368,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2369","image_path":"images/combination_2369.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2369_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2369_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2369_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2369_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2369_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2369,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5}],"canvas_size":[574,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2370","image_path":"images/combination_2370.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2370_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2370_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2370_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":"combination_2370_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2370_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2370,"target_cell_count":6,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[586,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2371","image_path":"images/combination_2371.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2371_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2371_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2371_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2371_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2371_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2371,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[582,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2372","image_path":"images/combination_2372.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2372_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2372_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2372_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2372_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2372_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2372,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10}],"canvas_size":[575,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2373","image_path":"images/combination_2373.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2373_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2373_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2373_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2373_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2373_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2373,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2374","image_path":"images/combination_2374.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2374_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2374_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2374_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2374_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2374_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2374,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2375","image_path":"images/combination_2375.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2375_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2375_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_2375_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":"combination_2375_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2375_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2375,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[595,440],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2376","image_path":"images/combination_2376.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2376_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2376_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2376_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2376_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2376_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2376,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3],[2,4],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[579,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2377","image_path":"images/combination_2377.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2377_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2377_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2377_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2377_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2377_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2377,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[557,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2378","image_path":"images/combination_2378.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2378_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2378_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2378_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2378_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2378_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2378,"target_cell_count":9,"target_cells":[[0,4],[0,5],[1,2],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[562,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2379","image_path":"images/combination_2379.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2379_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2379_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2379_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2379_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2379_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2379,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7}],"canvas_size":[576,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2380","image_path":"images/combination_2380.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2380_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2380_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2380_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":"combination_2380_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2380_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2380,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[563,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2381","image_path":"images/combination_2381.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2381_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2381_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2381_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2381_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2381,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[581,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2382","image_path":"images/combination_2382.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2382_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2382_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2382_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":"combination_2382_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2382_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2382,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[576,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2383","image_path":"images/combination_2383.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2383_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2383_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2383_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2383_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2383_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2383,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[574,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2384","image_path":"images/combination_2384.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2384_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2384_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2384_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2384_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2384_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2384,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[595,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2385","image_path":"images/combination_2385.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2385_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2385_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2385_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2385_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2385_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2385,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[588,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2386","image_path":"images/combination_2386.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2386_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2386_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2386_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2386_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2386_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2386,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[550,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2387","image_path":"images/combination_2387.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2387_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2387_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2387_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":"combination_2387_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2387_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2387,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,437],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2388","image_path":"images/combination_2388.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2388_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2388_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2388_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":"combination_2388_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2388_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2388,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[599,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2389","image_path":"images/combination_2389.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2389_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2389_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2389_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2389_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2389_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2389,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[581,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2390","image_path":"images/combination_2390.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2390_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2390_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2390_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":"combination_2390_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2390_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2390,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[564,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2391","image_path":"images/combination_2391.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2391_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2391_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2391_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2391_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2391_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2391,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[568,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2392","image_path":"images/combination_2392.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2392_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2392_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2392_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":"combination_2392_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2392_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2392,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2393","image_path":"images/combination_2393.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2393_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2393_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"D","question_id":"combination_2393_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2393_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2393,"target_cell_count":8,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[578,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2394","image_path":"images/combination_2394.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2394_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2394_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2394_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2394_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2394_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2394,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,2],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,2],[1,4],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[595,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2395","image_path":"images/combination_2395.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2395_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2395_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2395_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2395_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2395_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2395,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,2],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":7}],"canvas_size":[583,409],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2396","image_path":"images/combination_2396.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2396_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2396_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2396_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2396_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2396_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2396,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[554,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2397","image_path":"images/combination_2397.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2397_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2397_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2397_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":"combination_2397_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2397_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2397,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2398","image_path":"images/combination_2398.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2398_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2398_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2398_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":"combination_2398_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2398_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2398,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[596,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2399","image_path":"images/combination_2399.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2399_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2399_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2399_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2399_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2399_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2399,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[554,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2400","image_path":"images/combination_2400.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2400_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2400_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2400_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":"combination_2400_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2400_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2400,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,2],[2,1],[2,2],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[553,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2401","image_path":"images/combination_2401.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2401_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2401_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2401_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":"combination_2401_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2401_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2401,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[593,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2402","image_path":"images/combination_2402.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2402_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2402_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2402_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2402_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2402_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2402,"target_cell_count":8,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[555,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2403","image_path":"images/combination_2403.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2403_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2403_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2403_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":"combination_2403_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2403_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2403,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[4,1],[4,2],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[577,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2404","image_path":"images/combination_2404.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2404_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2404_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2404_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2404_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2404_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2404,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1]],[[0,0]]],"total_cell_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],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[565,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2405","image_path":"images/combination_2405.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2405_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2405_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2405_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":"combination_2405_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2405_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2405,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]]}
{"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],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[576,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2406","image_path":"images/combination_2406.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2406_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2406_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2406_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2406_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2406_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2406,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[574,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2407","image_path":"images/combination_2407.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2407_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2407_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2407_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2407_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2407_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2407,"target_cell_count":8,"target_cells":[[0,1],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[574,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2408","image_path":"images/combination_2408.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2408_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2408_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2408_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2408_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2408_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2408,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":8}],"canvas_size":[575,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2409","image_path":"images/combination_2409.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2409_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2409_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2409_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":"combination_2409_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2409_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2409,"target_cell_count":8,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[556,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2410","image_path":"images/combination_2410.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2410_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2410_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2410_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":"combination_2410_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2410_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2410,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[556,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2411","image_path":"images/combination_2411.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2411_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2411_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2411_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":"combination_2411_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2411_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2411,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[571,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2412","image_path":"images/combination_2412.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2412_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2412_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2412_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2412_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2412_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2412,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[577,440],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2413","image_path":"images/combination_2413.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2413_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2413_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2413_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":"combination_2413_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2413_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2413,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[560,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2414","image_path":"images/combination_2414.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2414_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2414_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2414_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":"combination_2414_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2414_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2414,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[584,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2415","image_path":"images/combination_2415.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2415_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2415_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2415_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2415_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2415_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2415,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[590,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2416","image_path":"images/combination_2416.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2416_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2416_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2416_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2416_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2416_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2416,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[582,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2417","image_path":"images/combination_2417.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2417_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2417_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2417_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":"combination_2417_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2417_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2417,"target_cell_count":8,"target_cells":[[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[600,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2418","image_path":"images/combination_2418.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2418_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2418_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2418_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":"combination_2418_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2418_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2418,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9}],"canvas_size":[552,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2419","image_path":"images/combination_2419.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2419_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2419_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2419_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2419_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2419_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2419,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[5,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[1,5]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[571,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2420","image_path":"images/combination_2420.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2420_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2420_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2420_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2420_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2420_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2420,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[551,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2421","image_path":"images/combination_2421.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2421_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2421_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2421_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2421_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2421_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2421,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[581,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2422","image_path":"images/combination_2422.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2422_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2422_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2422_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2422_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2422_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2422,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2423","image_path":"images/combination_2423.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2423_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2423_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2423_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":"combination_2423_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2423_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2423,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2424","image_path":"images/combination_2424.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2424_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2424_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2424_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":"combination_2424_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2424_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2424,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2425","image_path":"images/combination_2425.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2425_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2425_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2425_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":"combination_2425_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2425_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2425,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2426","image_path":"images/combination_2426.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2426_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2426_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2426_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2426_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2426_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2426,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,3],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":9}],"canvas_size":[592,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2427","image_path":"images/combination_2427.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2427_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2427_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_2427_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2427_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2427,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,2],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[4,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[570,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2428","image_path":"images/combination_2428.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2428_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2428_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2428_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2428_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2428_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2428,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[572,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2429","image_path":"images/combination_2429.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2429_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2429_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2429_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2429_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2429_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2429,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[557,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2430","image_path":"images/combination_2430.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2430_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2430_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2430_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2430_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2430_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2430,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2]]],"total_cell_count":10}],"canvas_size":[574,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2431","image_path":"images/combination_2431.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2431_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2431_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2431_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":"combination_2431_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2431_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2431,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[591,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2432","image_path":"images/combination_2432.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2432_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2432_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2432_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":"combination_2432_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2432_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2432,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[593,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2433","image_path":"images/combination_2433.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2433_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2433_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2433_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":"combination_2433_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2433_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2433,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2434","image_path":"images/combination_2434.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2434_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2434_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2434_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2434_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2434_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2434,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[592,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2435","image_path":"images/combination_2435.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2435_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2435_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_2435_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2435_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2435,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[600,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2436","image_path":"images/combination_2436.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2436_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2436_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2436_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":"combination_2436_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2436_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2436,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[582,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2437","image_path":"images/combination_2437.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2437_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2437_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2437_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2437_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2437_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2437,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[579,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2438","image_path":"images/combination_2438.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2438_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2438_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2438_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2438_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2438_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2438,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[1,5]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[551,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2439","image_path":"images/combination_2439.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2439_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2439_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2439_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":"combination_2439_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2439_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2439,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[2,5],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[581,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2440","image_path":"images/combination_2440.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2440_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2440_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2440_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2440_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2440_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2440,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[574,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2441","image_path":"images/combination_2441.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2441_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2441_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2441_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":"combination_2441_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2441_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2441,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[571,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2442","image_path":"images/combination_2442.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2442_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2442_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2442_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2442_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2442_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2442,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[577,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2443","image_path":"images/combination_2443.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2443_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2443_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2443_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":"combination_2443_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2443_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2443,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[579,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2444","image_path":"images/combination_2444.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2444_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2444_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2444_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2444_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2444_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2444,"target_cell_count":10,"target_cells":[[0,4],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[0,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[579,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2445","image_path":"images/combination_2445.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2445_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2445_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2445_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2445_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2445_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2445,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[573,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2446","image_path":"images/combination_2446.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2446_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2446_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2446_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2446_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2446_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2446,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[596,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2447","image_path":"images/combination_2447.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2447_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2447_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2447_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2447_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2447_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2447,"target_cell_count":9,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[580,411],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2448","image_path":"images/combination_2448.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2448_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2448_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2448_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":"combination_2448_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2448_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2448,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]]],"total_cell_count":10}],"canvas_size":[555,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2449","image_path":"images/combination_2449.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2449_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2449_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2449_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2449_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2449_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2449,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,2],[2,3],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[581,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2450","image_path":"images/combination_2450.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2450_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2450_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2450_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":"combination_2450_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2450_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2450,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[565,440],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2451","image_path":"images/combination_2451.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2451_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2451_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2451_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2451_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2451_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2451,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_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],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[562,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2452","image_path":"images/combination_2452.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2452_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2452_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2452_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2452_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2452_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2452,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[580,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2453","image_path":"images/combination_2453.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2453_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2453_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2453_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2453_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2453_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2453,"target_cell_count":7,"target_cells":[[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2454","image_path":"images/combination_2454.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2454_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2454_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2454_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2454_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2454_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2454,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,2],[2,3],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[580,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2455","image_path":"images/combination_2455.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2455_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2455_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2455_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2455_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2455_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2455,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2],[4,3],[4,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[586,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2456","image_path":"images/combination_2456.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2456_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2456_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2456_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":"combination_2456_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2456_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2456,"target_cell_count":8,"target_cells":[[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[552,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2457","image_path":"images/combination_2457.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2457_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2457_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2457_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2457_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2457_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2457,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[3,1],[3,3],[4,0],[4,1],[4,2],[4,3],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[590,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2458","image_path":"images/combination_2458.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2458_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2458_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2458_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":"combination_2458_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2458_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2458,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[572,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2459","image_path":"images/combination_2459.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2459_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2459_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2459_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2459_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2459_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2459,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,425],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2460","image_path":"images/combination_2460.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2460_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2460_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2460_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":"combination_2460_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2460_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2460,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2461","image_path":"images/combination_2461.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2461_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2461_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2461_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2461_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2461_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2461,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[558,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2462","image_path":"images/combination_2462.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2462_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2462_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2462_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":"combination_2462_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2462_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2462,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[557,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2463","image_path":"images/combination_2463.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2463_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2463_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2463_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2463_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2463_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2463,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[586,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2464","image_path":"images/combination_2464.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2464_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2464_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2464_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2464_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2464_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2464,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[583,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2465","image_path":"images/combination_2465.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2465_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2465_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2465_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":"combination_2465_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2465_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2465,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2466","image_path":"images/combination_2466.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2466_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2466_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2466_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2466_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2466_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2466,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":5}],"canvas_size":[562,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2467","image_path":"images/combination_2467.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2467_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2467_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2467_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2467_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2467_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2467,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[567,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2468","image_path":"images/combination_2468.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2468_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2468_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2468_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2468_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2468_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2468,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":6}],"canvas_size":[566,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2469","image_path":"images/combination_2469.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2469_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2469_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2469_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2469_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2469_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2469,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[4,0],[4,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[566,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2470","image_path":"images/combination_2470.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2470_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2470_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2470_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2470_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2470_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2470,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[576,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2471","image_path":"images/combination_2471.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2471_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2471_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2471_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2471_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2471_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2471,"target_cell_count":7,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[575,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2472","image_path":"images/combination_2472.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2472_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2472_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2472_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":"combination_2472_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2472_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2472,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[573,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2473","image_path":"images/combination_2473.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2473_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2473_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2473_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2473_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2473_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2473,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[577,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2474","image_path":"images/combination_2474.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2474_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2474_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2474_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2474_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2474_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2474,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2475","image_path":"images/combination_2475.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2475_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2475_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2475_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2475_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2475_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2475,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[600,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2476","image_path":"images/combination_2476.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2476_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2476_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2476_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2476_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2476_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2476,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[564,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2477","image_path":"images/combination_2477.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2477_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2477_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2477_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":"combination_2477_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2477_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2477,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[595,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2478","image_path":"images/combination_2478.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2478_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2478_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2478_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":"combination_2478_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2478_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2478,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[575,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2479","image_path":"images/combination_2479.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2479_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2479_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2479_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2479_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2479_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2479,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[590,405],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2480","image_path":"images/combination_2480.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2480_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2480_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2480_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2480_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2480_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2480,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10}],"canvas_size":[557,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2481","image_path":"images/combination_2481.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2481_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2481_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2481_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":"combination_2481_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2481_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2481,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":9}],"canvas_size":[562,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2482","image_path":"images/combination_2482.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2482_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2482_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2482_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2482_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2482_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2482,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3],[3,3],[3,4]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[0,4],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[584,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2483","image_path":"images/combination_2483.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2483_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2483_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2483_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2483_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2483_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2483,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,2],[1,3],[1,4],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2484","image_path":"images/combination_2484.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2484_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2484_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2484_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2484_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2484_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2484,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[550,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2485","image_path":"images/combination_2485.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2485_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2485_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2485_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":"combination_2485_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2485_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2485,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2486","image_path":"images/combination_2486.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2486_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2486_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2486_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2486_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2486_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2486,"target_cell_count":7,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[596,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2487","image_path":"images/combination_2487.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2487_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2487_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2487_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":"combination_2487_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2487_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2487,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":8}],"canvas_size":[572,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2488","image_path":"images/combination_2488.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2488_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2488_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2488_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2488_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2488_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2488,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2489","image_path":"images/combination_2489.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2489_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2489_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2489_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":"combination_2489_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2489_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2489,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2490","image_path":"images/combination_2490.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2490_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2490_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2490_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2490_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2490_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2490,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2491","image_path":"images/combination_2491.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2491_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2491_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2491_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":"combination_2491_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2491_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2491,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[578,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2492","image_path":"images/combination_2492.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2492_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2492_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2492_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2492_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2492_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2492,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2493","image_path":"images/combination_2493.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2493_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2493_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2493_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2493_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2493_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2493,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[594,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2494","image_path":"images/combination_2494.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2494_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2494_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_2494_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2494_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2494,"target_cell_count":7,"target_cells":[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[555,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2495","image_path":"images/combination_2495.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2495_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2495_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2495_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2495_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2495_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2495,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2496","image_path":"images/combination_2496.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2496_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2496_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2496_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":"combination_2496_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2496_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2496,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[578,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2497","image_path":"images/combination_2497.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2497_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2497_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2497_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":"combination_2497_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2497_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2497,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[561,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2498","image_path":"images/combination_2498.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2498_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2498_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2498_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2498_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2498_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2498,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8}],"canvas_size":[598,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2499","image_path":"images/combination_2499.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2499_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2499_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2499_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":"combination_2499_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2499_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2499,"target_cell_count":8,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2500","image_path":"images/combination_2500.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2500_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2500_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2500_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":"combination_2500_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2500_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2500,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[561,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2501","image_path":"images/combination_2501.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2501_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2501_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2501_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2501_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2501_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2501,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3]]],"total_cell_count":10}],"canvas_size":[559,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2502","image_path":"images/combination_2502.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2502_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2502_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2502_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2502_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2502_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2502,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3],[3,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[570,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2503","image_path":"images/combination_2503.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2503_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2503_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2503_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":"combination_2503_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2503_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2503,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[557,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2504","image_path":"images/combination_2504.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2504_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2504_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2504_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2504_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2504_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2504,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[569,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2505","image_path":"images/combination_2505.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2505_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2505_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2505_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":"combination_2505_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2505_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2505,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[598,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2506","image_path":"images/combination_2506.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2506_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2506_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2506_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":"combination_2506_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2506_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2506,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[586,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2507","image_path":"images/combination_2507.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2507_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2507_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2507_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":"combination_2507_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2507_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2507,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[559,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2508","image_path":"images/combination_2508.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2508_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2508_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2508_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":"combination_2508_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2508_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2508,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6}],"canvas_size":[581,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2509","image_path":"images/combination_2509.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2509_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2509_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2509_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2509_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2509_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2509,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[582,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2510","image_path":"images/combination_2510.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2510_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2510_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2510_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2510_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2510_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2510,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[595,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2511","image_path":"images/combination_2511.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2511_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2511_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2511_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":"combination_2511_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2511_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2511,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[596,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2512","image_path":"images/combination_2512.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2512_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2512_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2512_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":"combination_2512_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2512_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2512,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[573,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2513","image_path":"images/combination_2513.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2513_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2513_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2513_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2513_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2513_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2513,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[4,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[556,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2514","image_path":"images/combination_2514.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2514_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2514_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2514_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2514_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2514_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2514,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[3,0],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2515","image_path":"images/combination_2515.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2515_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2515_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2515_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2515_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2515_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2515,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2],[4,1],[4,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[570,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2516","image_path":"images/combination_2516.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2516_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2516_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2516_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2516_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2516_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2516,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[563,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2517","image_path":"images/combination_2517.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2517_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2517_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2517_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":"combination_2517_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2517_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2517,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[576,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2518","image_path":"images/combination_2518.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2518_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2518_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2518_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":"combination_2518_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2518_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2518,"target_cell_count":9,"target_cells":[[0,1],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8}],"canvas_size":[551,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2519","image_path":"images/combination_2519.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2519_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2519_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2519_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2519_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2519_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2519,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2520","image_path":"images/combination_2520.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2520_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2520_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2520_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2520_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2520_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2520,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[566,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2521","image_path":"images/combination_2521.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2521_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2521_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2521_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":"combination_2521_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2521_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2521,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[571,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2522","image_path":"images/combination_2522.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2522_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2522_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2522_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2522_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2522_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2522,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,4]],[[0,0]]],"total_cell_count":10}],"canvas_size":[556,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2523","image_path":"images/combination_2523.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2523_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2523_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2523_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2523_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2523_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2523,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[590,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2524","image_path":"images/combination_2524.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2524_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2524_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2524_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":"combination_2524_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2524_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2524,"target_cell_count":6,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[568,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2525","image_path":"images/combination_2525.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2525_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2525_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2525_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":"combination_2525_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2525_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2525,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[2,1],[3,1],[4,1],[5,1],[5,2],[6,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[564,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2526","image_path":"images/combination_2526.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2526_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2526_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2526_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2526_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2526_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2526,"target_cell_count":9,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[590,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2527","image_path":"images/combination_2527.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2527_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2527_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2527_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2527_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2527_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2527,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[567,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2528","image_path":"images/combination_2528.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2528_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2528_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2528_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":"combination_2528_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2528_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2528,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10}],"canvas_size":[567,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2529","image_path":"images/combination_2529.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2529_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2529_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2529_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2529_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2529_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2529,"target_cell_count":10,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[582,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2530","image_path":"images/combination_2530.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2530_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2530_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2530_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":"combination_2530_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2530_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2530,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2531","image_path":"images/combination_2531.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2531_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2531_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2531_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":"combination_2531_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2531_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2531,"target_cell_count":6,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2532","image_path":"images/combination_2532.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2532_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2532_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2532_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2532_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2532_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2532,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[593,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2533","image_path":"images/combination_2533.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2533_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2533_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2533_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2533_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2533_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2533,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1],[3,2]]],"total_cell_count":8}],"canvas_size":[584,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2534","image_path":"images/combination_2534.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2534_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2534_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2534_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2534_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2534_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2534,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[593,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2535","image_path":"images/combination_2535.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2535_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2535_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2535_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2535_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2535_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2535,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2536","image_path":"images/combination_2536.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2536_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2536_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2536_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2536_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2536_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2536,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[552,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2537","image_path":"images/combination_2537.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2537_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2537_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2537_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2537_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2537_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2537,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[589,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2538","image_path":"images/combination_2538.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2538_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2538_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2538_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2538_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2538_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2538,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[600,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2539","image_path":"images/combination_2539.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2539_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2539_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2539_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":"combination_2539_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2539_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2539,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[552,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2540","image_path":"images/combination_2540.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2540_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2540_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2540_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2540_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2540_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2540,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[584,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2541","image_path":"images/combination_2541.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2541_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2541_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2541_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2541_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2541_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2541,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[554,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2542","image_path":"images/combination_2542.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2542_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2542_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2542_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":"combination_2542_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2542_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2542,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[550,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2543","image_path":"images/combination_2543.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2543_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2543_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2543_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2543_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2543_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2543,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0],[4,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[4,1]]],"total_cell_count":9}],"canvas_size":[585,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2544","image_path":"images/combination_2544.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2544_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2544_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2544_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":"combination_2544_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2544_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2544,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[579,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2545","image_path":"images/combination_2545.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2545_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2545_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2545_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2545_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2545_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2545,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":8}],"canvas_size":[571,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2546","image_path":"images/combination_2546.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2546_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2546_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2546_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":"combination_2546_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2546_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2546,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[570,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2547","image_path":"images/combination_2547.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2547_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2547_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2547_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":"combination_2547_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2547_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2547,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[599,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2548","image_path":"images/combination_2548.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2548_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2548_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2548_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2548_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2548_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2548,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[588,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2549","image_path":"images/combination_2549.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2549_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2549_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2549_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":"combination_2549_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2549_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2549,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[3,2],[3,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]],"total_cell_count":9}],"canvas_size":[561,434],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2550","image_path":"images/combination_2550.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2550_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2550_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2550_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2550_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2550_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2550,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[587,439],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2551","image_path":"images/combination_2551.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2551_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2551_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2551_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":"combination_2551_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2551_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2551,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2552","image_path":"images/combination_2552.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2552_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2552_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2552_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2552_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2552_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2552,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[596,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2553","image_path":"images/combination_2553.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2553_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2553_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2553_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2553_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2553_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2553,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[570,410],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2554","image_path":"images/combination_2554.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2554_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2554_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2554_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2554_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2554_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2554,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":9}],"canvas_size":[569,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2555","image_path":"images/combination_2555.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2555_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2555_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2555_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2555_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2555_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2555,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[556,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2556","image_path":"images/combination_2556.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2556_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2556_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2556_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":"combination_2556_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2556_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2556,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[550,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2557","image_path":"images/combination_2557.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2557_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2557_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2557_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":"combination_2557_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2557_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2557,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[582,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2558","image_path":"images/combination_2558.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2558_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2558_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2558_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":"combination_2558_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2558_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2558,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[597,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2559","image_path":"images/combination_2559.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2559_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2559_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2559_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":"combination_2559_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2559_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2559,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[578,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2560","image_path":"images/combination_2560.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2560_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2560_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2560_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":"combination_2560_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2560_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2560,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":9}],"canvas_size":[559,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2561","image_path":"images/combination_2561.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2561_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2561_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2561_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2561_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2561_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2561,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[3,2],[3,3],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2562","image_path":"images/combination_2562.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2562_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2562_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2562_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2562_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2562_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2562,"target_cell_count":9,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2],[4,0],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[585,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2563","image_path":"images/combination_2563.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2563_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2563_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2563_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2563_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2563_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2563,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[556,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2564","image_path":"images/combination_2564.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2564_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2564_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2564_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2564_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2564_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2564,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2565","image_path":"images/combination_2565.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2565_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2565_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2565_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":"combination_2565_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2565_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2565,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2566","image_path":"images/combination_2566.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2566_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2566_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2566_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":"combination_2566_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2566_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2566,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[600,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2567","image_path":"images/combination_2567.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2567_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2567_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2567_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2567_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2567_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2567,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[586,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2568","image_path":"images/combination_2568.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2568_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2568_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2568_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":"combination_2568_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2568_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2568,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6}],"canvas_size":[582,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2569","image_path":"images/combination_2569.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2569_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2569_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2569_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2569_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2569_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2569,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[591,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2570","image_path":"images/combination_2570.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2570_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2570_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2570_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2570_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2570_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2570,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[559,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2571","image_path":"images/combination_2571.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2571_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2571_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2571_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":"combination_2571_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2571_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2571,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[553,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2572","image_path":"images/combination_2572.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2572_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2572_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2572_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":"combination_2572_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2572_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2572,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2573","image_path":"images/combination_2573.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2573_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2573_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2573_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2573_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2573_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2573,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,2],[2,3],[3,2],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":5}],"canvas_size":[552,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2574","image_path":"images/combination_2574.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2574_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2574_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2574_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":"combination_2574_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2574_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2574,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7}],"canvas_size":[569,405],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2575","image_path":"images/combination_2575.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2575_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2575_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2575_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":"combination_2575_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2575_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2575,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[594,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2576","image_path":"images/combination_2576.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2576_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2576_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2576_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":"combination_2576_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2576_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2576,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9}],"canvas_size":[589,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2577","image_path":"images/combination_2577.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2577_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2577_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2577_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2577_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2577_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2577,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[578,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2578","image_path":"images/combination_2578.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2578_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2578_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2578_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":"combination_2578_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2578_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2578,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2579","image_path":"images/combination_2579.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2579_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2579_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2579_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2579_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2579_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2579,"target_cell_count":8,"target_cells":[[0,3],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2580","image_path":"images/combination_2580.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2580_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2580_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2580_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":"combination_2580_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2580_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2580,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[558,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2581","image_path":"images/combination_2581.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2581_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2581_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2581_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2581_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2581_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2581,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[596,408],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2582","image_path":"images/combination_2582.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2582_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2582_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2582_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":"combination_2582_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2582_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2582,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[571,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2583","image_path":"images/combination_2583.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2583_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2583_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2583_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":"combination_2583_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2583_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2583,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[569,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2584","image_path":"images/combination_2584.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2584_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2584_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2584_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":"combination_2584_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2584_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2584,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[556,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2585","image_path":"images/combination_2585.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2585_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2585_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2585_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":"combination_2585_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2585_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2585,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[568,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2586","image_path":"images/combination_2586.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2586_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2586_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2586_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":"combination_2586_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2586_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2586,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[566,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2587","image_path":"images/combination_2587.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2587_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2587_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"A","question_id":"combination_2587_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2587_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2587,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2588","image_path":"images/combination_2588.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2588_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2588_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2588_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2588_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2588_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2588,"target_cell_count":7,"target_cells":[[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2589","image_path":"images/combination_2589.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2589_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2589_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2589_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":"combination_2589_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2589_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2589,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[595,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2590","image_path":"images/combination_2590.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2590_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2590_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2590_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":"combination_2590_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2590_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2590,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2591","image_path":"images/combination_2591.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2591_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2591_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2591_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":"combination_2591_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2591_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2591,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[585,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2592","image_path":"images/combination_2592.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2592_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2592_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2592_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2592_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2592_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2592,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[579,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2593","image_path":"images/combination_2593.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2593_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2593_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2593_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":"combination_2593_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2593_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2593,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[570,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2594","image_path":"images/combination_2594.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2594_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2594_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2594_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2594_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2594_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2594,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[594,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2595","image_path":"images/combination_2595.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2595_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2595_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2595_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":"combination_2595_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2595_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2595,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[559,423],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2596","image_path":"images/combination_2596.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2596_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2596_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2596_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":"combination_2596_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2596_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2596,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0],[3,1],[4,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[584,403],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2597","image_path":"images/combination_2597.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2597_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2597_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2597_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2597_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2597_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2597,"target_cell_count":9,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[596,444],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2598","image_path":"images/combination_2598.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2598_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2598_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2598_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":"combination_2598_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2598_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2598,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,3],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[582,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2599","image_path":"images/combination_2599.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2599_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2599_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2599_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2599_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2599_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2599,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[582,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2600","image_path":"images/combination_2600.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2600_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2600_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2600_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2600_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2600_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2600,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2601","image_path":"images/combination_2601.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2601_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2601_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_2601_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2601_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2601,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[555,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2602","image_path":"images/combination_2602.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2602_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2602_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2602_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":"combination_2602_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2602_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2602,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[569,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2603","image_path":"images/combination_2603.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2603_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2603_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2603_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":"combination_2603_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2603_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2603,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[550,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2604","image_path":"images/combination_2604.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2604_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2604_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2604_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2604_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2604,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,400],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2605","image_path":"images/combination_2605.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2605_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2605_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2605_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2605_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2605_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2605,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[576,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2606","image_path":"images/combination_2606.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2606_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2606_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2606_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":"combination_2606_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2606_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2606,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,1],[2,1],[2,2],[2,3],[3,1],[4,0],[4,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,442],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2607","image_path":"images/combination_2607.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2607_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2607_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_2607_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2607_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2607,"target_cell_count":10,"target_cells":[[0,0],[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[596,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2608","image_path":"images/combination_2608.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2608_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2608_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2608_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2608_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2608_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2608,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[3,3],[4,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[552,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2609","image_path":"images/combination_2609.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2609_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2609_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2609_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2609_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2609_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2609,"target_cell_count":10,"target_cells":[[0,3],[1,3],[1,4],[1,5],[2,1],[2,2],[2,3],[3,0],[3,1],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[581,424],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2610","image_path":"images/combination_2610.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2610_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2610_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2610_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2610_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2610_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2610,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[576,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2611","image_path":"images/combination_2611.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2611_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2611_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2611_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2611_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2611_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2611,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[561,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2612","image_path":"images/combination_2612.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2612_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2612_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2612_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2612_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2612_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2612,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[567,424],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2613","image_path":"images/combination_2613.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2613_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2613_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2613_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":"combination_2613_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2613_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2613,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[558,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2614","image_path":"images/combination_2614.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2614_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2614_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2614_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":"combination_2614_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2614_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2614,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[585,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2615","image_path":"images/combination_2615.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2615_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2615_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2615_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":"combination_2615_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2615_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2615,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[579,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2616","image_path":"images/combination_2616.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2616_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2616_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2616_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2616_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2616_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2616,"target_cell_count":6,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[554,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2617","image_path":"images/combination_2617.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2617_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2617_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2617_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":"combination_2617_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2617_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2617,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[597,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2618","image_path":"images/combination_2618.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2618_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2618_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2618_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":"combination_2618_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2618_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2618,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9}],"canvas_size":[585,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2619","image_path":"images/combination_2619.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2619_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2619_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2619_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2619_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2619_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2619,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[594,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2620","image_path":"images/combination_2620.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2620_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2620_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2620_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2620_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2620_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2620,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[575,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2621","image_path":"images/combination_2621.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2621_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2621_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2621_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2621_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2621_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2621,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[566,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2622","image_path":"images/combination_2622.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2622_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2622_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2622_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2622_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2622_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2622,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[551,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2623","image_path":"images/combination_2623.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2623_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2623_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2623_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2623_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2623_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2623,"target_cell_count":9,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2624","image_path":"images/combination_2624.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2624_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2624_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2624_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2624_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2624_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2624,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2625","image_path":"images/combination_2625.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2625_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2625_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2625_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":"combination_2625_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2625_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2625,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2626","image_path":"images/combination_2626.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2626_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2626_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2626_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2626_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2626_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2626,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[591,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2627","image_path":"images/combination_2627.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2627_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2627_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2627_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2627_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2627_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2627,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[568,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2628","image_path":"images/combination_2628.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2628_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2628_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_2628_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2628_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2628,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[574,432],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2629","image_path":"images/combination_2629.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2629_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2629_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2629_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":"combination_2629_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2629_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2629,"target_cell_count":10,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[598,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2630","image_path":"images/combination_2630.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2630_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2630_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2630_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":"combination_2630_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2630_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2630,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[590,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2631","image_path":"images/combination_2631.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2631_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2631_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2631_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2631_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2631_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2631,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[565,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2632","image_path":"images/combination_2632.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2632_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2632_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2632_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2632_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2632_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2632,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[582,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2633","image_path":"images/combination_2633.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2633_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2633_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2633_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2633_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2633_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2633,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[589,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2634","image_path":"images/combination_2634.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2634_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2634_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2634_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":"combination_2634_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2634_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2634,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1],[2,2],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[595,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2635","image_path":"images/combination_2635.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2635_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2635_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2635_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":"combination_2635_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2635_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2635,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7}],"canvas_size":[588,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2636","image_path":"images/combination_2636.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2636_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2636_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2636_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":"combination_2636_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2636_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2636,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[566,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2637","image_path":"images/combination_2637.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2637_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2637_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2637_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2637_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2637_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2637,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[582,443],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2638","image_path":"images/combination_2638.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2638_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2638_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2638_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2638_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2638_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2638,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[585,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2639","image_path":"images/combination_2639.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2639_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2639_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2639_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":"combination_2639_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2639_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2639,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2640","image_path":"images/combination_2640.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2640_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2640_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2640_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":"combination_2640_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2640_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2640,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,3],[2,4]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[598,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2641","image_path":"images/combination_2641.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2641_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2641_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2641_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2641_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2641_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2641,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[586,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2642","image_path":"images/combination_2642.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2642_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2642_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2642_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2642_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2642_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2642,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[562,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2643","image_path":"images/combination_2643.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2643_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2643_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2643_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2643_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2643_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2643,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2644","image_path":"images/combination_2644.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2644_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2644_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2644_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":"combination_2644_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2644_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2644,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":8}],"canvas_size":[585,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2645","image_path":"images/combination_2645.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2645_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2645_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2645_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":"combination_2645_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2645_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2645,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0],[3,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[551,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2646","image_path":"images/combination_2646.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2646_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2646_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2646_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2646_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2646_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2646,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[572,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2647","image_path":"images/combination_2647.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2647_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2647_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2647_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":"combination_2647_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2647_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2647,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7}],"canvas_size":[573,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2648","image_path":"images/combination_2648.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2648_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2648_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2648_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":"combination_2648_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2648_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2648,"target_cell_count":7,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":8}],"canvas_size":[558,418],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2649","image_path":"images/combination_2649.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2649_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2649_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2649_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2649_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2649_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2649,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":7}],"canvas_size":[594,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2650","image_path":"images/combination_2650.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2650_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2650_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2650_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":"combination_2650_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2650_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2650,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,430],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2651","image_path":"images/combination_2651.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2651_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2651_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2651_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2651_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2651_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2651,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2652","image_path":"images/combination_2652.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2652_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2652_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2652_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":"combination_2652_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2652_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2652,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[590,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2653","image_path":"images/combination_2653.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2653_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2653_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2653_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":"combination_2653_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2653_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2653,"target_cell_count":9,"target_cells":[[0,4],[0,5],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,0],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,0]]],"total_cell_count":10}],"canvas_size":[577,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2654","image_path":"images/combination_2654.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2654_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2654_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2654_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2654_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2654_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2654,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[558,448],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2655","image_path":"images/combination_2655.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2655_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2655_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2655_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":"combination_2655_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2655_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2655,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[0,2]]],"total_cell_count":7}],"canvas_size":[558,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2656","image_path":"images/combination_2656.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2656_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2656_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2656_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2656_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2656_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2656,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1],[4,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":7}],"canvas_size":[553,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2657","image_path":"images/combination_2657.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2657_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2657_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2657_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":"combination_2657_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2657_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2657,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,1],[4,1],[4,2],[5,0],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[552,431],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2658","image_path":"images/combination_2658.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2658_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2658_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2658_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":"combination_2658_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2658_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2658,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[582,404],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2659","image_path":"images/combination_2659.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2659_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2659_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_2659_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2659_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2659,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[556,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2660","image_path":"images/combination_2660.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2660_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2660_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2660_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":"combination_2660_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2660_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2660,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[571,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2661","image_path":"images/combination_2661.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2661_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2661_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2661_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2661_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2661_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2661,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[593,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2662","image_path":"images/combination_2662.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2662_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2662_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2662_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":"combination_2662_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2662_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2662,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[587,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2663","image_path":"images/combination_2663.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2663_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2663_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2663_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":"combination_2663_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2663_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2663,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[589,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2664","image_path":"images/combination_2664.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2664_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2664_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2664_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2664_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2664_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2664,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_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],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9}],"canvas_size":[593,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2665","image_path":"images/combination_2665.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2665_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2665_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2665_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2665_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2665_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2665,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[3,0]]],"total_cell_count":10}],"canvas_size":[568,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2666","image_path":"images/combination_2666.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2666_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2666_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2666_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2666_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2666_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2666,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[557,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2667","image_path":"images/combination_2667.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2667_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2667_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2667_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":"combination_2667_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2667_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2667,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[569,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2668","image_path":"images/combination_2668.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2668_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2668_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2668_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2668_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2668_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2668,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[567,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2669","image_path":"images/combination_2669.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2669_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2669_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2669_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2669_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2669_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2669,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[588,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2670","image_path":"images/combination_2670.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2670_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2670_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2670_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":"combination_2670_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2670_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2670,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[557,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2671","image_path":"images/combination_2671.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2671_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2671_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_2671_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":"combination_2671_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2671_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2671,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2672","image_path":"images/combination_2672.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2672_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2672_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2672_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2672_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2672_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2672,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[563,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2673","image_path":"images/combination_2673.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2673_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2673_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2673_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":"combination_2673_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2673_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2673,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[598,402],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2674","image_path":"images/combination_2674.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2674_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2674_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2674_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":"combination_2674_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2674_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2674,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[587,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2675","image_path":"images/combination_2675.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2675_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2675_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2675_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":"combination_2675_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2675_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2675,"target_cell_count":9,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[566,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2676","image_path":"images/combination_2676.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2676_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2676_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2676_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2676_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2676_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2676,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2677","image_path":"images/combination_2677.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2677_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2677_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2677_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":"combination_2677_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2677_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2677,"target_cell_count":7,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[557,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2678","image_path":"images/combination_2678.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2678_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2678_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2678_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":"combination_2678_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2678_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2678,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[585,436],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2679","image_path":"images/combination_2679.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2679_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2679_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2679_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":"combination_2679_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2679_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2679,"target_cell_count":8,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[583,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2680","image_path":"images/combination_2680.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2680_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2680_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2680_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2680_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2680_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2680,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2],[1,3]]],"total_cell_count":9}],"canvas_size":[553,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2681","image_path":"images/combination_2681.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2681_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2681_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"C","question_id":"combination_2681_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2681_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2681,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2682","image_path":"images/combination_2682.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2682_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2682_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2682_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2682_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2682_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2682,"target_cell_count":9,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[597,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2683","image_path":"images/combination_2683.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2683_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2683_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2683_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2683_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2683_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2683,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[570,432],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2684","image_path":"images/combination_2684.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2684_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2684_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2684_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":"combination_2684_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2684_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2684,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[564,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2685","image_path":"images/combination_2685.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2685_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2685_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2685_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2685_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2685_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2685,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[4,1],[4,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0],[4,0],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1],[4,1],[4,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[564,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2686","image_path":"images/combination_2686.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2686_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2686_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2686_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":"combination_2686_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2686_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2686,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[579,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2687","image_path":"images/combination_2687.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2687_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2687_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2687_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":"combination_2687_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2687_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2687,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[590,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2688","image_path":"images/combination_2688.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2688_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2688_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2688_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":"combination_2688_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2688_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2688,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[552,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2689","image_path":"images/combination_2689.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2689_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2689_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2689_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":"combination_2689_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2689_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2689,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[571,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2690","image_path":"images/combination_2690.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2690_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2690_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2690_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":"combination_2690_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2690_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2690,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[572,409],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2691","image_path":"images/combination_2691.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2691_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2691_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2691_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2691_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2691,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[566,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2692","image_path":"images/combination_2692.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2692_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2692_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2692_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":"combination_2692_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2692_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2692,"target_cell_count":9,"target_cells":[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8}],"canvas_size":[595,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2693","image_path":"images/combination_2693.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2693_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2693_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2693_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2693_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2693_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2693,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[1,0]]],"total_cell_count":7}],"canvas_size":[569,435],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2694","image_path":"images/combination_2694.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2694_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2694_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2694_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2694_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2694_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2694,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,0],[3,1],[3,2],[4,0],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[593,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2695","image_path":"images/combination_2695.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2695_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2695_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"4","question_id":"combination_2695_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":"combination_2695_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2695_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2695,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[589,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2696","image_path":"images/combination_2696.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2696_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2696_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2696_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2696_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2696_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2696,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,2],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[597,442],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2697","image_path":"images/combination_2697.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2697_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2697_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2697_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":"combination_2697_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2697_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2697,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[564,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2698","image_path":"images/combination_2698.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2698_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2698_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2698_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":"combination_2698_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2698_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2698,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2699","image_path":"images/combination_2699.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2699_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2699_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2699_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":"combination_2699_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2699_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2699,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[565,443],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2700","image_path":"images/combination_2700.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2700_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2700_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2700_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2700_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2700_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2700,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,441],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2701","image_path":"images/combination_2701.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2701_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2701_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2701_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2701_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2701_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2701,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[560,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2702","image_path":"images/combination_2702.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2702_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2702_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2702_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":"combination_2702_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2702_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2702,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[576,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2703","image_path":"images/combination_2703.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2703_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2703_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2703_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2703_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2703_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2703,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[587,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2704","image_path":"images/combination_2704.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2704_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2704_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2704_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":"combination_2704_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2704_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2704,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":7}],"canvas_size":[561,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2705","image_path":"images/combination_2705.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2705_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2705_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2705_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":"combination_2705_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2705_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2705,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2706","image_path":"images/combination_2706.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2706_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2706_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2706_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2706_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2706_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2706,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[572,413],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2707","image_path":"images/combination_2707.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2707_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2707_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_2707_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2707_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2707,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[596,412],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2708","image_path":"images/combination_2708.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2708_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2708_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2708_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2708_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2708_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2708,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4]]],"total_cell_count":10}],"canvas_size":[591,411],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2709","image_path":"images/combination_2709.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2709_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2709_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2709_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2709_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2709,"target_cell_count":10,"target_cells":[[0,2],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3],[3,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[582,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2710","image_path":"images/combination_2710.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2710_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2710_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2710_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":"combination_2710_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2710_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2710,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[2,4],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3],[3,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[566,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.53,"id":"combination_2711","image_path":"images/combination_2711.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2711_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2711_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2711_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":"combination_2711_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2711_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2711,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[567,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2712","image_path":"images/combination_2712.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2712_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2712_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2712_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2712_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2712_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2712,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[580,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2713","image_path":"images/combination_2713.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2713_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2713_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2713_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2713_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2713_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2713,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[578,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2714","image_path":"images/combination_2714.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2714_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2714_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2714_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":"combination_2714_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2714_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2714,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[594,426],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2715","image_path":"images/combination_2715.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2715_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2715_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2715_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":"combination_2715_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2715_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2715,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[550,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2716","image_path":"images/combination_2716.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2716_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2716_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2716_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":"combination_2716_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2716_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2716,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[589,415],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2717","image_path":"images/combination_2717.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2717_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2717_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2717_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2717_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2717_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2717,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[563,400],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2718","image_path":"images/combination_2718.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2718_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2718_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2718_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2718_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2718_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2718,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,435],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2719","image_path":"images/combination_2719.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2719_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2719_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2719_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":"combination_2719_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2719_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2719,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,4],[1,3],[1,4],[2,1],[2,2],[2,3],[3,0],[3,1],[3,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,3],[2,4],[3,4]],[[0,0]]],"total_cell_count":10}],"canvas_size":[562,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2720","image_path":"images/combination_2720.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2720_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2720_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2720_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2720_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2720_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2720,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,3],[1,1],[1,2],[1,3],[2,1],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[584,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2721","image_path":"images/combination_2721.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2721_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2721_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2721_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2721_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2721_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2721,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[569,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2722","image_path":"images/combination_2722.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2722_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2722_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2722_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":"combination_2722_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2722_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2722,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[2,3]]],"total_cell_count":8}],"canvas_size":[593,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2723","image_path":"images/combination_2723.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2723_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2723_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2723_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":"combination_2723_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2723_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2723,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[593,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2724","image_path":"images/combination_2724.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2724_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2724_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2724_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":"combination_2724_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2724_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2724,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3],[2,4]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]],"total_cell_count":10}],"canvas_size":[579,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2725","image_path":"images/combination_2725.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2725_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2725_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2725_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2725_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2725_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2725,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[560,401],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2726","image_path":"images/combination_2726.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2726_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2726_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2726_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":"combination_2726_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2726_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2726,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,1],[3,1],[3,2],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[568,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2727","image_path":"images/combination_2727.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2727_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2727_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2727_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":"combination_2727_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2727_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2727,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[552,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2728","image_path":"images/combination_2728.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2728_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2728_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2728_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":"combination_2728_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2728_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2728,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6}],"canvas_size":[558,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2729","image_path":"images/combination_2729.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2729_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2729_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2729_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":"combination_2729_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2729_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2729,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":7}],"canvas_size":[551,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2730","image_path":"images/combination_2730.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2730_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2730_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2730_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":"combination_2730_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2730_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2730,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[592,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2731","image_path":"images/combination_2731.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2731_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2731_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2731_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2731_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2731_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2731,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[2,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[596,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2732","image_path":"images/combination_2732.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2732_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2732_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2732_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2732_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2732_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2732,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[596,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2733","image_path":"images/combination_2733.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2733_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2733_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2733_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":"combination_2733_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2733_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2733,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8}],"canvas_size":[550,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2734","image_path":"images/combination_2734.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2734_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2734_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2734_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":"combination_2734_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2734_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2734,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":6}],"canvas_size":[566,403],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2735","image_path":"images/combination_2735.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2735_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2735_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2735_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2735_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2735_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2735,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,427],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2736","image_path":"images/combination_2736.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2736_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2736_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2736_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2736_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2736_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2736,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[572,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2737","image_path":"images/combination_2737.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2737_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2737_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2737_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":"combination_2737_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2737_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2737,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[575,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2738","image_path":"images/combination_2738.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2738_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2738_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2738_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2738_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2738_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2738,"target_cell_count":9,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8}],"canvas_size":[575,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2739","image_path":"images/combination_2739.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2739_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2739_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2739_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2739_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2739_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2739,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,1]]],"total_cell_count":9}],"canvas_size":[590,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2740","image_path":"images/combination_2740.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2740_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2740_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2740_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":"combination_2740_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2740_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2740,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[0,5],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[578,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2741","image_path":"images/combination_2741.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2741_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2741_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2741_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":"combination_2741_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2741_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2741,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2742","image_path":"images/combination_2742.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2742_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2742_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2742_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":"combination_2742_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2742_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2742,"target_cell_count":7,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[562,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2743","image_path":"images/combination_2743.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2743_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2743_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2743_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":"combination_2743_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2743_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2743,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[571,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2744","image_path":"images/combination_2744.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2744_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2744_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2744_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2744_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2744_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2744,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[580,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2745","image_path":"images/combination_2745.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2745_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2745_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2745_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":"combination_2745_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2745_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2745,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]],"total_cell_count":9}],"canvas_size":[558,419],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2746","image_path":"images/combination_2746.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2746_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2746_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2746_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2746_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2746_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2746,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[4,1],[4,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,411],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2747","image_path":"images/combination_2747.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2747_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2747_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2747_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":"combination_2747_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2747_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2747,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,418],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2748","image_path":"images/combination_2748.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2748_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2748_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2748_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2748_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2748_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2748,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[558,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2749","image_path":"images/combination_2749.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2749_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2749_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2749_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2749_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2749_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2749,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[559,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2750","image_path":"images/combination_2750.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2750_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2750_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2750_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2750_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2750_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2750,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2751","image_path":"images/combination_2751.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2751_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2751_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2751_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2751_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2751,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[588,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2752","image_path":"images/combination_2752.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2752_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2752_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2752_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":"combination_2752_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2752_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2752,"target_cell_count":6,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[563,421],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2753","image_path":"images/combination_2753.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2753_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2753_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"D","question_id":"combination_2753_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2753_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2753,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"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]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[587,421],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2754","image_path":"images/combination_2754.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2754_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2754_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2754_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":"combination_2754_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2754_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2754,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_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],[0,2],[0,3],[1,1],[1,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[596,429],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2755","image_path":"images/combination_2755.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2755_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2755_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"4","question_id":"combination_2755_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":"combination_2755_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2755_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2755,"target_cell_count":10,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":10}],"canvas_size":[581,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2756","image_path":"images/combination_2756.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2756_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2756_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2756_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2756_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2756_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2756,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2757","image_path":"images/combination_2757.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2757_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2757_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2757_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2757_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2757_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2757,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[569,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2758","image_path":"images/combination_2758.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2758_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2758_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2758_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2758_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2758_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2758,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2759","image_path":"images/combination_2759.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2759_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2759_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2759_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2759_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2759_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2759,"target_cell_count":8,"target_cells":[[0,2],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4],[2,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[591,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2760","image_path":"images/combination_2760.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2760_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2760_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2760_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2760_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2760_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2760,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,3],[0,4],[1,1],[1,2],[1,3],[1,4],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2761","image_path":"images/combination_2761.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2761_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2761_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2761_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":"combination_2761_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2761_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2761,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_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]],[[0,0],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":10}],"canvas_size":[560,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2762","image_path":"images/combination_2762.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2762_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2762_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2762_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":"combination_2762_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2762_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2762,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2763","image_path":"images/combination_2763.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2763_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2763_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2763_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2763_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2763_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2763,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[580,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2764","image_path":"images/combination_2764.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2764_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2764_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2764_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2764_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2764_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2764,"target_cell_count":9,"target_cells":[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[554,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2765","image_path":"images/combination_2765.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2765_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2765_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2765_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2765_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2765_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2765,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1],[3,2],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[581,403],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2766","image_path":"images/combination_2766.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2766_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2766_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2766_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":"combination_2766_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2766_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2766,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[581,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2767","image_path":"images/combination_2767.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2767_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2767_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2767_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2767_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2767_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2767,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[598,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2768","image_path":"images/combination_2768.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2768_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2768_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2768_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2768_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2768,"target_cell_count":8,"target_cells":[[0,0],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[560,405],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2769","image_path":"images/combination_2769.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2769_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2769_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2769_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2769_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2769_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2769,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[557,429],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2770","image_path":"images/combination_2770.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2770_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2770_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2770_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2770_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2770_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2770,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":10}],"canvas_size":[563,414],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2771","image_path":"images/combination_2771.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2771_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2771_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2771_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":"combination_2771_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2771_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2771,"target_cell_count":10,"target_cells":[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[578,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2772","image_path":"images/combination_2772.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2772_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2772_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2772_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":"combination_2772_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2772_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2772,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[0,3],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7}],"canvas_size":[561,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2773","image_path":"images/combination_2773.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2773_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2773_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2773_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2773_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2773_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2773,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":8}],"canvas_size":[587,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2774","image_path":"images/combination_2774.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2774_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2774_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2774_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2774_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2774_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2774,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[5,0],[6,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[1,3],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,428],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2775","image_path":"images/combination_2775.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2775_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2775_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2775_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2775_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2775_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2775,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[572,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2776","image_path":"images/combination_2776.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2776_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2776_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2776_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2776_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2776,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,3],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[587,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2777","image_path":"images/combination_2777.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2777_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2777_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2777_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2777_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2777_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2777,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8}],"canvas_size":[569,415],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2778","image_path":"images/combination_2778.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2778_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2778_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2778_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2778_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2778_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2778,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[595,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2779","image_path":"images/combination_2779.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2779_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2779_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2779_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":"combination_2779_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2779_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2779,"target_cell_count":7,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[586,444],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2780","image_path":"images/combination_2780.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2780_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2780_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2780_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":"combination_2780_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2780_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2780,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7}],"canvas_size":[567,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2781","image_path":"images/combination_2781.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2781_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2781_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2781_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":"combination_2781_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2781_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2781,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[571,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2782","image_path":"images/combination_2782.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2782_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2782_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2782_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2782_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2782_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2782,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10}],"canvas_size":[589,422],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2783","image_path":"images/combination_2783.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2783_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2783_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2783_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2783_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2783_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2783,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[557,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2784","image_path":"images/combination_2784.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2784_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2784_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2784_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2784_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2784_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2784,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[571,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2785","image_path":"images/combination_2785.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2785_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2785_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2785_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":"combination_2785_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2785_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2785,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[577,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2786","image_path":"images/combination_2786.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2786_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2786_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2786_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2786_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2786_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2786,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10}],"canvas_size":[594,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2787","image_path":"images/combination_2787.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2787_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2787_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2787_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":"combination_2787_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2787_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2787,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[573,415],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2788","image_path":"images/combination_2788.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2788_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2788_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2788_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":"combination_2788_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2788_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2788,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,1],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[599,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2789","image_path":"images/combination_2789.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2789_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2789_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2789_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2789_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2789_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2789,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[554,450],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2790","image_path":"images/combination_2790.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2790_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2790_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2790_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2790_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2790_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2790,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[595,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2791","image_path":"images/combination_2791.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2791_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2791_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2791_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2791_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2791_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2791,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[558,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2792","image_path":"images/combination_2792.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2792_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2792_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2792_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":"combination_2792_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2792_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2792,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2793","image_path":"images/combination_2793.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2793_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2793_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2793_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":"combination_2793_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2793_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2793,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[552,437],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2794","image_path":"images/combination_2794.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2794_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2794_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2794_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":"combination_2794_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2794_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2794,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[1,4],[1,5]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[0,4],[0,5],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[592,424],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2795","image_path":"images/combination_2795.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2795_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2795_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2795_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":"combination_2795_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2795_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2795,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[2,4],[2,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2796","image_path":"images/combination_2796.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2796_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2796_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2796_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2796_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2796_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2796,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[589,446],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2797","image_path":"images/combination_2797.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2797_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2797_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2797_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2797_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2797_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2797,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":10}],"canvas_size":[595,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2798","image_path":"images/combination_2798.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2798_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2798_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2798_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":"combination_2798_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2798_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2798,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2],[3,3],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[600,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2799","image_path":"images/combination_2799.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2799_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2799_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2799_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":"combination_2799_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2799_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2799,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,1],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2800","image_path":"images/combination_2800.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2800_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2800_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2800_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":"combination_2800_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2800_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2800,"target_cell_count":8,"target_cells":[[0,0],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[1,3],[2,0],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[579,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2801","image_path":"images/combination_2801.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2801_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2801_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2801_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2801_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2801_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2801,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7}],"canvas_size":[570,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2802","image_path":"images/combination_2802.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2802_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2802_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2802_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":"combination_2802_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2802_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2802,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,419],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2803","image_path":"images/combination_2803.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2803_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2803_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2803_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2803_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2803_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2803,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[568,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2804","image_path":"images/combination_2804.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2804_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2804_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2804_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":"combination_2804_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2804_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2804,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,1],[1,1],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[558,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2805","image_path":"images/combination_2805.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2805_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2805_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2805_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":"combination_2805_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2805_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2805,"target_cell_count":9,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[588,441],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2806","image_path":"images/combination_2806.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2806_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2806_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2806_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2806_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2806_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2806,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,1],[0,2],[0,3],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1],[1,2],[1,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[4,1]]],"total_cell_count":10}],"canvas_size":[585,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2807","image_path":"images/combination_2807.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2807_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2807_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2807_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2807_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2807_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2807,"target_cell_count":10,"target_cells":[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[559,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2808","image_path":"images/combination_2808.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2808_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2808_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2808_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":"combination_2808_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2808_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2808,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,2],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6}],"canvas_size":[592,443],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2809","image_path":"images/combination_2809.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2809_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2809_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2809_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2809_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2809_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2809,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[574,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2810","image_path":"images/combination_2810.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2810_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2810_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2810_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":"combination_2810_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2810_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2810,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,423],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2811","image_path":"images/combination_2811.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2811_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2811_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2811_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":"combination_2811_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2811_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2811,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,0],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[591,407],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2812","image_path":"images/combination_2812.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2812_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2812_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2812_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2812_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2812_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2812,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[586,438],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2813","image_path":"images/combination_2813.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2813_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2813_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2813_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":"combination_2813_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2813_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2813,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_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],[2,0],[3,0],[3,1],[4,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[585,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2814","image_path":"images/combination_2814.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2814_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2814_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2814_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2814_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2814_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2814,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[4,1]]],"total_cell_count":9}],"canvas_size":[600,447],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2815","image_path":"images/combination_2815.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2815_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2815_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2815_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2815_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2815_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2815,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[578,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2816","image_path":"images/combination_2816.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2816_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2816_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2816_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":"combination_2816_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2816_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2816,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[582,423],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2817","image_path":"images/combination_2817.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2817_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2817_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2817_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2817_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2817_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2817,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[554,407],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2818","image_path":"images/combination_2818.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2818_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2818_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2818_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":"combination_2818_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2818_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2818,"target_cell_count":9,"target_cells":[[0,1],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[565,416],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2819","image_path":"images/combination_2819.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2819_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2819_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2819_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":"combination_2819_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2819_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2819,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[2,0],[3,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[588,410],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2820","image_path":"images/combination_2820.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2820_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2820_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2820_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":"combination_2820_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2820_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2820,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[3,0],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[576,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2821","image_path":"images/combination_2821.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2821_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2821_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2821_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2821_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2821_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2821,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,2],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":10}],"canvas_size":[575,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2822","image_path":"images/combination_2822.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2822_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2822_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"4","question_id":"combination_2822_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":"combination_2822_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2822_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2822,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[568,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2823","image_path":"images/combination_2823.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2823_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2823_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2823_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2823_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2823_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2823,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[562,438],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2824","image_path":"images/combination_2824.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2824_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2824_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2824_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2824_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2824_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2824,"target_cell_count":9,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,3]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_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],[0,2],[0,3],[1,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":7}],"canvas_size":[561,409],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2825","image_path":"images/combination_2825.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2825_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2825_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2825_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":"combination_2825_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2825_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2825,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[561,445],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2826","image_path":"images/combination_2826.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2826_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2826_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2826_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":"combination_2826_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2826_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2826,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1]],[[0,1],[1,1],[2,1],[3,0],[3,1]]],"total_cell_count":9}],"canvas_size":[557,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2827","image_path":"images/combination_2827.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2827_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2827_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2827_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":"combination_2827_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2827_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2827,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[577,430],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2828","image_path":"images/combination_2828.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2828_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2828_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2828_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2828_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2828_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2828,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[566,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2829","image_path":"images/combination_2829.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2829_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2829_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2829_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2829_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2829_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2829,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":9}],"canvas_size":[590,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2830","image_path":"images/combination_2830.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2830_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2830_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2830_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":"combination_2830_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2830_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2830,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2831","image_path":"images/combination_2831.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2831_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2831_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2831_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2831_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2831_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2831,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[553,421],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2832","image_path":"images/combination_2832.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2832_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2832_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2832_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2832_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2832_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2832,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[598,435],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2833","image_path":"images/combination_2833.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2833_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2833_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2833_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":"combination_2833_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2833_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2833,"target_cell_count":6,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[580,449],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2834","image_path":"images/combination_2834.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2834_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2834_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2834_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2834_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2834_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2834,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[563,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2835","image_path":"images/combination_2835.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2835_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2835_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2835_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2835_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2835_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2835,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[587,435],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2836","image_path":"images/combination_2836.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2836_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2836_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2836_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":"combination_2836_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2836_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2836,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[569,407],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2837","image_path":"images/combination_2837.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2837_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2837_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2837_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":"combination_2837_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2837_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2837,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[595,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2838","image_path":"images/combination_2838.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2838_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2838_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2838_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2838_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2838_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2838,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[576,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2839","image_path":"images/combination_2839.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2839_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2839_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2839_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2839_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2839_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2839,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[598,422],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2840","image_path":"images/combination_2840.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2840_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2840_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2840_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":"combination_2840_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2840_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2840,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[572,445],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2841","image_path":"images/combination_2841.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2841_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2841_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2841_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2841_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2841_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2841,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[550,420],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2842","image_path":"images/combination_2842.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2842_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2842_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2842_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2842_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2842_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2842,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,2],[1,3],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[586,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2843","image_path":"images/combination_2843.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2843_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2843_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2843_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":"combination_2843_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2843_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2843,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[578,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2844","image_path":"images/combination_2844.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2844_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2844_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2844_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2844_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2844_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2844,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[562,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2845","image_path":"images/combination_2845.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2845_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2845_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2845_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2845_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2845_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2845,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[573,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2846","image_path":"images/combination_2846.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2846_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2846_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2846_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2846_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2846_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2846,"target_cell_count":9,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[594,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2847","image_path":"images/combination_2847.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2847_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2847_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2847_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2847_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2847_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2847,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7}],"canvas_size":[584,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2848","image_path":"images/combination_2848.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2848_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2848_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2848_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2848_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2848_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2848,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[578,429],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2849","image_path":"images/combination_2849.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2849_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2849_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2849_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2849_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2849_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2849,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[551,433],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2850","image_path":"images/combination_2850.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2850_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2850_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2850_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2850_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2850_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2850,"target_cell_count":8,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1]]],"total_cell_count":6}],"canvas_size":[570,410],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2851","image_path":"images/combination_2851.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2851_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2851_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2851_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2851_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2851_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2851,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,450],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2852","image_path":"images/combination_2852.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2852_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2852_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2852_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2852_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2852_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2852,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[560,402],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2853","image_path":"images/combination_2853.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2853_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2853_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2853_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2853_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2853_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2853,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,0],[2,1],[2,2],[2,3],[3,0],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0],[1,0],[2,0]]],"total_cell_count":9}],"canvas_size":[555,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2854","image_path":"images/combination_2854.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2854_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2854_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2854_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2854_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2854_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2854,"target_cell_count":10,"target_cells":[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":8}],"canvas_size":[582,418],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2855","image_path":"images/combination_2855.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2855_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2855_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2855_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2855_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2855_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2855,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":6}],"canvas_size":[589,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2856","image_path":"images/combination_2856.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2856_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2856_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2856_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":"combination_2856_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2856_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2856,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":7}],"canvas_size":[596,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2857","image_path":"images/combination_2857.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2857_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2857_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2857_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":"combination_2857_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2857_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2857,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[588,414],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2858","image_path":"images/combination_2858.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2858_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2858_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_2858_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2858_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2858,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[581,445],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2859","image_path":"images/combination_2859.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2859_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2859_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2859_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2859_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2859_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2859,"target_cell_count":9,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[592,406],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2860","image_path":"images/combination_2860.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2860_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2860_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2860_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":"combination_2860_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2860_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2860,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[570,437],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2861","image_path":"images/combination_2861.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2861_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2861_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2861_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2861_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2861_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2861,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[592,413],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2862","image_path":"images/combination_2862.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2862_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2862_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2862_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2862_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2862_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2862,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[583,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2863","image_path":"images/combination_2863.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2863_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2863_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2863_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2863_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2863_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2863,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[585,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2864","image_path":"images/combination_2864.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2864_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2864_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2864_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":"combination_2864_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2864_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2864,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6}],"canvas_size":[588,408],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2865","image_path":"images/combination_2865.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2865_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2865_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2865_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2865_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2865_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2865,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[580,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2866","image_path":"images/combination_2866.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2866_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2866_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2866_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2866_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2866_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2866,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6}],"canvas_size":[552,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2867","image_path":"images/combination_2867.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2867_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2867_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2867_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2867_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2867_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2867,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[580,442],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2868","image_path":"images/combination_2868.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2868_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2868_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2868_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":"combination_2868_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2868_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2868,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[581,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2869","image_path":"images/combination_2869.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2869_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2869_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2869_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":"combination_2869_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2869_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2869,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,5],[1,0],[1,1],[1,2],[1,3],[1,4],[1,5],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[576,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2870","image_path":"images/combination_2870.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2870_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2870_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"combination_2870_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2870_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2870,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[592,441],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2871","image_path":"images/combination_2871.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2871_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2871_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2871_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2871_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2871_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2871,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2],[3,2]]],"total_cell_count":7}],"canvas_size":[599,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2872","image_path":"images/combination_2872.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2872_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2872_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2872_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":"combination_2872_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2872_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2872,"target_cell_count":7,"target_cells":[[0,2],[1,2],[2,2],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,2],[2,3]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[591,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2873","image_path":"images/combination_2873.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2873_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2873_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"4","question_id":"combination_2873_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":"combination_2873_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2873_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2873,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[3,1],[4,0],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[561,423],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2874","image_path":"images/combination_2874.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2874_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2874_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2874_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":"combination_2874_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2874_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2874,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":6}],"canvas_size":[561,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2875","image_path":"images/combination_2875.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2875_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2875_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2875_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2875_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2875_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2875,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[584,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2876","image_path":"images/combination_2876.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2876_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2876_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2876_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2876_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2876_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2876,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]],"total_cell_count":7}],"canvas_size":[574,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2877","image_path":"images/combination_2877.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2877_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2877_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2877_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2877_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2877_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2877,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[0,4],[1,4],[1,5]]],"total_cell_count":9}],"canvas_size":[559,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2878","image_path":"images/combination_2878.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2878_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2878_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2878_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":"combination_2878_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2878_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2878,"target_cell_count":9,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[551,421],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2879","image_path":"images/combination_2879.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2879_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2879_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2879_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2879_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2879_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2879,"target_cell_count":6,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,2],[2,2]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[581,449],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2880","image_path":"images/combination_2880.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2880_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2880_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2880_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2880_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2880_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2880,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[600,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2881","image_path":"images/combination_2881.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2881_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2881_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2881_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2881_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2881_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2881,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2],[1,3]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5}],"canvas_size":[559,442],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2882","image_path":"images/combination_2882.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2882_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2882_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2882_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":"combination_2882_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2882_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2882,"target_cell_count":6,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[600,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2883","image_path":"images/combination_2883.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2883_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2883_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2883_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":"combination_2883_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2883_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2883,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0],[2,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[558,434],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2884","image_path":"images/combination_2884.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2884_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2884_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2884_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":"combination_2884_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2884_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2884,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,0],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[553,412],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2885","image_path":"images/combination_2885.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2885_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2885_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2885_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2885_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2885_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2885,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[567,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2886","image_path":"images/combination_2886.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2886_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2886_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2886_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":"combination_2886_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2886_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2886,"target_cell_count":7,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[589,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2887","image_path":"images/combination_2887.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2887_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2887_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2887_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":"combination_2887_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2887_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2887,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[568,416],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2888","image_path":"images/combination_2888.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2888_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2888_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2888_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2888_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2888_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2888,"target_cell_count":10,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[1,4],[2,4]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2]]],"total_cell_count":9}],"canvas_size":[585,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2889","image_path":"images/combination_2889.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2889_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2889_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2889_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2889_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2889_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2889,"target_cell_count":10,"target_cells":[[0,4],[1,0],[1,1],[1,2],[1,3],[1,4],[2,2],[2,3],[2,4],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[566,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2890","image_path":"images/combination_2890.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2890_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2890_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2890_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2890_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2890_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2890,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[3,1],[3,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,2],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2],[4,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[573,400],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2891","image_path":"images/combination_2891.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2891_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2891_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2891_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":"combination_2891_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2891_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2891,"target_cell_count":9,"target_cells":[[0,2],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2],[3,3],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,426],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2892","image_path":"images/combination_2892.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2892_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2892_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2892_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":"combination_2892_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2892_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2892,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[4,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[2,2],[3,1],[3,2],[4,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[564,448],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2893","image_path":"images/combination_2893.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2893_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2893_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2893_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2893_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2893_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2893,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2]]],"total_cell_count":9}],"canvas_size":[586,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2894","image_path":"images/combination_2894.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2894_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2894_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2894_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":"combination_2894_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2894_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2894,"target_cell_count":9,"target_cells":[[0,0],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":6}],"canvas_size":[586,446],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2895","image_path":"images/combination_2895.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2895_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2895_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2895_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2895_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2895_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2895,"target_cell_count":6,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[576,420],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2896","image_path":"images/combination_2896.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2896_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2896_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2896_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":"combination_2896_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2896_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2896,"target_cell_count":7,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[2,1],[2,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":7}],"canvas_size":[564,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2897","image_path":"images/combination_2897.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2897_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2897_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2897_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":"combination_2897_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2897_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2897,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[560,411],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2898","image_path":"images/combination_2898.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2898_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2898_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2898_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2898_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2898_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2898,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[583,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2899","image_path":"images/combination_2899.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2899_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2899_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2899_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2899_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2899_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2899,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[0,1]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[568,448],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2900","image_path":"images/combination_2900.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2900_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2900_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2900_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":"combination_2900_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2900_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2900,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[556,447],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2901","image_path":"images/combination_2901.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2901_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2901_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2901_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2901_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2901_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2901,"target_cell_count":8,"target_cells":[[0,4],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[1,2],[2,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6}],"canvas_size":[588,436],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2902","image_path":"images/combination_2902.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2902_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2902_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2902_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":"combination_2902_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2902_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2902,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[556,432],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2903","image_path":"images/combination_2903.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2903_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2903_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2903_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2903_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2903_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2903,"target_cell_count":6,"target_cells":[[0,3],[0,4],[1,0],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[594,446],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2904","image_path":"images/combination_2904.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2904_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2904_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2904_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":"combination_2904_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2904_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2904,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[592,410],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2905","image_path":"images/combination_2905.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2905_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2905_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2905_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2905_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2905_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2905,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[2,2]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[557,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2906","image_path":"images/combination_2906.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2906_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2906_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2906_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2906_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2906_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2906,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,0],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[584,415],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2907","image_path":"images/combination_2907.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2907_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2907_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2907_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2907_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2907_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2907,"target_cell_count":6,"target_cells":[[0,1],[1,1],[1,2],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8}],"canvas_size":[595,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2908","image_path":"images/combination_2908.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2908_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2908_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2908_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2908_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2908_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2908,"target_cell_count":8,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[596,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2909","image_path":"images/combination_2909.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2909_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2909_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2909_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2909_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2909_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2909,"target_cell_count":10,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,418],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2910","image_path":"images/combination_2910.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2910_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2910_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2910_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":"combination_2910_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2910_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2910,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0],[1,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[580,443],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2911","image_path":"images/combination_2911.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2911_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2911_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2911_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2911_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2911_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2911,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2],[2,3],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[599,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2912","image_path":"images/combination_2912.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2912_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2912_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2912_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2912_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2912_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2912,"target_cell_count":7,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1],[4,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0],[4,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[568,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2913","image_path":"images/combination_2913.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2913_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2913_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2913_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":"combination_2913_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2913_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2913,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[3,0]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2],[3,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[597,448],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2914","image_path":"images/combination_2914.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2914_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2914_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"combination_2914_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2914_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2914,"target_cell_count":10,"target_cells":[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":6}],"canvas_size":[575,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2915","image_path":"images/combination_2915.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2915_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2915_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2915_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":"combination_2915_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2915_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2915,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[581,414],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2916","image_path":"images/combination_2916.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2916_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2916_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2916_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2916_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2916_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2916,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[555,430],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2917","image_path":"images/combination_2917.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2917_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2917_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2917_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":"combination_2917_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2917_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2917,"target_cell_count":6,"target_cells":[[0,0],[1,0],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":8}],"canvas_size":[553,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2918","image_path":"images/combination_2918.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2918_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2918_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2918_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2918_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2918_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2918,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3],[3,3]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,3],[2,1],[2,2],[2,3],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":9}],"canvas_size":[557,407],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2919","image_path":"images/combination_2919.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2919_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2919_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2919_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":"combination_2919_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2919_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2919,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,3],[2,4],[2,5],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,428],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2920","image_path":"images/combination_2920.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2920_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2920_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"A","question_id":"combination_2920_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2920_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2920,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[3,2]],[[0,0],[0,1]]],"total_cell_count":10}],"canvas_size":[554,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2921","image_path":"images/combination_2921.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2921_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2921_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2921_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":"combination_2921_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2921_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2921,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[3,0],[3,1],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[550,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2922","image_path":"images/combination_2922.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2922_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2922_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"C","question_id":"combination_2922_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2922_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2922,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[591,444],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2923","image_path":"images/combination_2923.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2923_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2923_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2923_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2923_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2923_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2923,"target_cell_count":10,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[575,439],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2924","image_path":"images/combination_2924.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2924_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2924_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2924_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":"combination_2924_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2924_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2924,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8}],"canvas_size":[590,416],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2925","image_path":"images/combination_2925.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2925_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2925_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2925_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2925_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2925_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2925,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1]],[[0,0],[0,1],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,3],[2,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[595,427],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2926","image_path":"images/combination_2926.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2926_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2926_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2926_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":"combination_2926_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2926_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2926,"target_cell_count":10,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[587,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2927","image_path":"images/combination_2927.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2927_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2927_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2927_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2927_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2927_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2927,"target_cell_count":7,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3],[1,4],[2,4]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,3],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[572,436],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.64,"id":"combination_2928","image_path":"images/combination_2928.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2928_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2928_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2928_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2928_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2928_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2928,"target_cell_count":10,"target_cells":[[0,3],[0,4],[1,3],[1,4],[1,5],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8}],"canvas_size":[567,401],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2929","image_path":"images/combination_2929.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2929_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2929_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2929_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":"combination_2929_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2929_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2929,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2],[2,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[600,430],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2930","image_path":"images/combination_2930.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2930_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2930_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2930_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":"combination_2930_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2930_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2930,"target_cell_count":9,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,1],[2,2],[2,3],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[3,1],[3,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,1],[1,0],[1,1],[2,1],[2,2],[3,2]]],"total_cell_count":9}],"canvas_size":[571,433],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2931","image_path":"images/combination_2931.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2931_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2931_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_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":"B","question_id":"combination_2931_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2931_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2931,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]],"total_cell_count":8}],"canvas_size":[572,401],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2932","image_path":"images/combination_2932.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2932_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2932_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2932_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":"combination_2932_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2932_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2932,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":6}],"canvas_size":[568,406],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2933","image_path":"images/combination_2933.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2933_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2933_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2933_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":"combination_2933_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2933_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2933,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1]]],"total_cell_count":5}],"canvas_size":[574,422],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2934","image_path":"images/combination_2934.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2934_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2934_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2934_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":"combination_2934_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2934_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2934,"target_cell_count":6,"target_cells":[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0]],[[0,0],[0,1],[1,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2935","image_path":"images/combination_2935.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2935_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2935_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2935_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":"combination_2935_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2935_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2935,"target_cell_count":9,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[5,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1],[1,3],[1,4]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[1,2],[2,1],[2,2],[2,3]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[588,413],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2936","image_path":"images/combination_2936.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2936_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2936_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2936_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2936_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2936_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2936,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1],[3,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,1],[1,1],[2,0],[2,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,1],[1,2],[1,3],[1,4],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,1]],[[0,0],[0,1],[1,1],[2,1]]],"total_cell_count":10}],"canvas_size":[594,426],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2937","image_path":"images/combination_2937.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2937_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2937_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2937_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":"combination_2937_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2937_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2937,"target_cell_count":10,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1],[3,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,0],[0,1],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":9}],"canvas_size":[555,416],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2938","image_path":"images/combination_2938.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2938_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2938_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2938_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2938_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2938_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2938,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0]],[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":9}],"canvas_size":[587,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2939","image_path":"images/combination_2939.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2939_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2939_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2939_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2939_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2939_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2939,"target_cell_count":9,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[3,3],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[595,424],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2940","image_path":"images/combination_2940.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2940_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2940_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2940_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2940_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2940_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2940,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":9}],"canvas_size":[578,431],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2941","image_path":"images/combination_2941.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2941_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2941_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2941_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2941_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2941_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2941,"target_cell_count":9,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3],[3,4]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,2],[1,0],[1,1],[1,2],[1,3],[2,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[590,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2942","image_path":"images/combination_2942.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2942_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2942_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2942_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2942_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2942_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2942,"target_cell_count":8,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,0],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[582,438],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2943","image_path":"images/combination_2943.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2943_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2943_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2943_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2943_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2943_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2943,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[551,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2944","image_path":"images/combination_2944.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2944_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2944_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2944_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":"combination_2944_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2944_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2944,"target_cell_count":7,"target_cells":[[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2],[2,3]],[[0,0]]],"total_cell_count":7}],"canvas_size":[597,419],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2945","image_path":"images/combination_2945.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2945_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2945_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2945_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":"combination_2945_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2945_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2945,"target_cell_count":7,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[572,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2946","image_path":"images/combination_2946.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2946_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2946_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2946_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":"combination_2946_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2946_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2946,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3]],[[0,0]]],"total_cell_count":9}],"canvas_size":[565,437],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2947","image_path":"images/combination_2947.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2947_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2947_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_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":"B","question_id":"combination_2947_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2947_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2947,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2],[2,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[2,1]],[[0,0],[0,1],[0,2],[0,3],[1,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[2,2],[3,2]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0]],[[0,1],[1,0],[1,1],[1,2],[1,3]]],"total_cell_count":10}],"canvas_size":[567,417],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2948","image_path":"images/combination_2948.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2948_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2948_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2948_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2948_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2948_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2948,"target_cell_count":10,"target_cells":[[0,1],[1,1],[2,0],[2,1],[2,2],[2,3],[2,4],[3,3],[3,4],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,1],[1,0],[1,1]]],"total_cell_count":8}],"canvas_size":[599,428],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2949","image_path":"images/combination_2949.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2949_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2949_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2949_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2949_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2949_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2949,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1],[2,2]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]]],"total_cell_count":8}],"canvas_size":[570,425],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2950","image_path":"images/combination_2950.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2950_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2950_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2950_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2950_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2950_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2950,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[597,450],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2951","image_path":"images/combination_2951.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2951_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2951_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2951_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2951_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2951_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2951,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[557,403],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2952","image_path":"images/combination_2952.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2952_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2952_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2952_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":"combination_2952_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2952_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2952,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[2,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":5}],"canvas_size":[574,436],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2953","image_path":"images/combination_2953.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2953_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2953_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2953_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":"combination_2953_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2953_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2953,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[2,0],[2,1],[2,2]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[1,0],[2,0],[3,0],[3,1],[3,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2]],[[0,0]],[[0,0],[0,1],[0,2],[1,2]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0]],[[0,0],[0,1],[0,2],[1,0],[2,0],[3,0]]],"total_cell_count":10}],"canvas_size":[589,405],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2954","image_path":"images/combination_2954.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2954_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2954_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2954_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":"combination_2954_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2954_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2954,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,0],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[591,402],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2955","image_path":"images/combination_2955.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2955_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2955_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2955_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":"combination_2955_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2955_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2955,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,2],[1,2],[2,0],[2,1],[2,2]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[587,402],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.475,"id":"combination_2956","image_path":"images/combination_2956.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2956_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2956_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2956_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2956_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2956_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2956,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[551,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2957","image_path":"images/combination_2957.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2957_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2957_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2957_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2957_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2957_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2957,"target_cell_count":7,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":6}],"canvas_size":[573,446],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2958","image_path":"images/combination_2958.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2958_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2958_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2958_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2958_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2958_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2958,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":5}],"canvas_size":[596,420],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2959","image_path":"images/combination_2959.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2959_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2959_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2959_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":"combination_2959_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2959_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2959,"target_cell_count":6,"target_cells":[[0,1],[0,2],[1,1],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,1],[1,0],[1,1],[2,0],[3,0],[3,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[554,431],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2960","image_path":"images/combination_2960.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2960_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2960_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2960_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2960_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2960_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2960,"target_cell_count":9,"target_cells":[[0,1],[0,3],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7}],"canvas_size":[570,404],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2961","image_path":"images/combination_2961.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2961_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2961_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2961_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2961_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2961_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2961,"target_cell_count":8,"target_cells":[[0,1],[1,1],[2,0],[2,1],[3,1],[3,2],[4,2],[4,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,1],[3,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1],[1,0]]],"total_cell_count":7}],"canvas_size":[559,438],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2962","image_path":"images/combination_2962.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2962_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2962_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2962_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":"combination_2962_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2962_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2962,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,1],[1,2]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,0]]],"total_cell_count":6}],"canvas_size":[597,401],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2963","image_path":"images/combination_2963.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2963_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2963_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination_2963_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":"combination_2963_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2963_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2963,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[3,1]],[[0,0]]],"total_cell_count":6}],"canvas_size":[592,441],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2964","image_path":"images/combination_2964.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2964_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2964_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2964_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2964_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2964_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2964,"target_cell_count":6,"target_cells":[[0,1],[1,0],[1,1],[2,1],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,1],[1,2]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[1,0]]],"total_cell_count":6}],"canvas_size":[563,413],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2965","image_path":"images/combination_2965.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2965_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2965_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2965_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2965_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2965_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2965,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1]],[[0,0],[0,1]]],"total_cell_count":6}],"canvas_size":[588,428],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2966","image_path":"images/combination_2966.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2966_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2966_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2966_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2966_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2966_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2966,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[1,3]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,1]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[599,406],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2967","image_path":"images/combination_2967.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2967_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2967_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2967_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":"combination_2967_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2967_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2967,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[0,3],[0,4],[1,0],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[553,429],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2968","image_path":"images/combination_2968.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2968_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2968_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2968_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2968_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2968_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2968,"target_cell_count":6,"target_cells":[[0,3],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0],[3,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1]],[[0,0]],[[0,1],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[582,449],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.355,"id":"combination_2969","image_path":"images/combination_2969.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2969_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2969_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2969_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2969_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2969_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2969,"target_cell_count":7,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0]],[[0,0]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[0,3],[1,1],[1,2],[1,3],[2,3]]],"total_cell_count":9}],"canvas_size":[593,439],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.585,"id":"combination_2970","image_path":"images/combination_2970.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2970_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2970_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination_2970_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2970_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2970_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2970,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[2,1],[2,2],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[587,403],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2971","image_path":"images/combination_2971.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2971_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2971_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2971_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":"combination_2971_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2971_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2971,"target_cell_count":6,"target_cells":[[0,0],[1,0],[1,1],[1,2],[1,3],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,2],[2,2]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[1,0],[2,0]]],"total_cell_count":10}],"canvas_size":[555,447],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2972","image_path":"images/combination_2972.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2972_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2972_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2972_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2972_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2972_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2972,"target_cell_count":10,"target_cells":[[0,0],[1,0],[1,3],[2,0],[2,1],[2,2],[2,3],[3,1],[3,2],[3,3]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[3,0],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[1,1],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[1,4],[1,5],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[3,1],[3,2],[3,3]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[599,427],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2973","image_path":"images/combination_2973.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2973_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2973_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2973_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":"combination_2973_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2973_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2973,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,1],[1,1],[2,0],[2,1],[3,1]]],"total_cell_count":9}],"canvas_size":[552,412],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2974","image_path":"images/combination_2974.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2974_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2974_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2974_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2974_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2974_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2974,"target_cell_count":9,"target_cells":[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1]],[[0,0],[0,1],[1,0]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[592,425],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2975","image_path":"images/combination_2975.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2975_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2975_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination_2975_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2975_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2975_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2975,"target_cell_count":10,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0],[3,1],[4,1],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,0]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[0,3],[0,4],[1,0],[1,1],[2,1],[2,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,1]],[[0,0],[1,0]],[[0,0],[1,0]]],"total_cell_count":9}],"canvas_size":[569,419],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.525,"id":"combination_2976","image_path":"images/combination_2976.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2976_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2976_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2976_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2976_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2976_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2976,"target_cell_count":9,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1],[3,2],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,3],[2,3]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1]],[[0,2],[1,2],[2,0],[2,1],[2,2]]],"total_cell_count":9}],"canvas_size":[578,439],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2977","image_path":"images/combination_2977.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2977_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2977_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2977_q3","question_text":"Does candidate C have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2977_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2977_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2977,"target_cell_count":10,"target_cells":[[0,3],[1,3],[2,0],[2,1],[2,2],[2,3],[2,4],[2,5],[3,4],[3,5]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[2,0],[3,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[1,0],[1,1],[2,0],[3,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1]]],"total_cell_count":8}],"canvas_size":[586,409],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2978","image_path":"images/combination_2978.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2978_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2978_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2978_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":"combination_2978_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2978_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2978,"target_cell_count":8,"target_cells":[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[0,4],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,0],[0,1],[0,2],[0,3],[1,0],[1,2],[2,0]]],"total_cell_count":10}],"canvas_size":[559,449],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2979","image_path":"images/combination_2979.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2979_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2979_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2979_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2979_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2979_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2979,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[2,4],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[2,0],[2,1],[3,0],[3,1],[4,1],[4,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1],[3,1],[4,1]],[[0,0]],[[0,0]]],"total_cell_count":10}],"canvas_size":[583,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2980","image_path":"images/combination_2980.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2980_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2980_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2980_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2980_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2980_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2980,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[0,1],[1,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[1,0]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2]],[[0,0],[0,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[591,450],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2981","image_path":"images/combination_2981.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2981_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2981_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2981_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":"combination_2981_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2981_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2981,"target_cell_count":10,"target_cells":[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[2,3],[2,4],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,1],[1,0],[1,1],[1,2]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1],[1,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[0,1],[0,2],[1,1]]],"total_cell_count":7}],"canvas_size":[596,432],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2982","image_path":"images/combination_2982.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2982_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2982_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2982_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2982_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2982_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2982,"target_cell_count":8,"target_cells":[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,1],[1,1],[2,0],[2,1],[3,0],[4,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]],[[0,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,1],[1,2],[1,3]],[[0,0]],[[0,0]]],"total_cell_count":8}],"canvas_size":[572,434],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2983","image_path":"images/combination_2983.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2983_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2983_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2983_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination_2983_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2983_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2983,"target_cell_count":8,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1]]],"total_cell_count":5},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":6}],"canvas_size":[556,433],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2984","image_path":"images/combination_2984.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2984_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2984_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2984_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":"combination_2984_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2984_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2984,"target_cell_count":6,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[2,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,0]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[0,3],[1,2],[1,3]],[[0,0],[1,0],[1,1]]],"total_cell_count":9}],"canvas_size":[586,422],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2985","image_path":"images/combination_2985.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2985_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2985_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2985_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":"combination_2985_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2985_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2985,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[1,3],[1,4],[2,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0],[1,0],[1,1]],[[0,0]]],"total_cell_count":7}],"canvas_size":[556,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2986","image_path":"images/combination_2986.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2986_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2986_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination_2986_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":"combination_2986_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2986_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2986,"target_cell_count":8,"target_cells":[[0,1],[1,0],[1,1],[1,2],[1,3],[2,0],[2,1],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[2,3],[2,4]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[0,3],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1],[1,2],[1,3]],[[0,0],[1,0],[2,0],[2,1]],[[0,0]]],"total_cell_count":10}],"canvas_size":[551,431],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2987","image_path":"images/combination_2987.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2987_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2987_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2987_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":"combination_2987_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2987_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2987,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[3,2],[4,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0]],[[0,0],[0,1]]],"total_cell_count":6},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":6}],"canvas_size":[593,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2988","image_path":"images/combination_2988.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2988_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2988_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2988_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":"combination_2988_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2988_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2988,"target_cell_count":6,"target_cells":[[0,1],[1,1],[2,1],[2,2],[3,0],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[1,2]],[[0,0]],[[0,0],[1,0]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,1],[1,0],[1,1],[1,2],[2,1],[2,2]]],"total_cell_count":7}],"canvas_size":[584,420],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2989","image_path":"images/combination_2989.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2989_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2989_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination_2989_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination_2989_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"disconnected","question_id":"combination_2989_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2989,"target_cell_count":7,"target_cells":[[0,0],[0,1],[0,2],[1,0],[2,0],[2,1],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,1],[1,2],[2,0],[2,2],[3,0],[3,1],[3,2]],[[0,0]]],"total_cell_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,1],[2,2],[3,1]],[[0,0]]],"total_cell_count":9},{"choice_label":"C","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[0,2],[1,0],[1,2],[2,1],[2,2]],[[0,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[0,1],[1,0],[2,0],[3,0],[4,0]]],"total_cell_count":9}],"canvas_size":[554,447],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.465,"id":"combination_2990","image_path":"images/combination_2990.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination_2990_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2990_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2990_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":"combination_2990_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2990_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2990,"target_cell_count":9,"target_cells":[[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0]],[[0,0]]],"total_cell_count":5},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[0,1],[1,0],[1,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0]],[[0,1],[0,2],[1,0],[1,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,1],[1,2]],[[0,0]]],"total_cell_count":6}],"canvas_size":[586,427],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.36,"id":"combination_2991","image_path":"images/combination_2991.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2991_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2991_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination_2991_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":"combination_2991_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2991_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2991,"target_cell_count":6,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2]],[[0,1],[1,0],[1,1]]],"total_cell_count":9},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3]],[[0,0],[0,1],[1,1]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[0,1],[0,2],[1,0]]],"total_cell_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,3]],[[0,1],[1,0],[1,1]]],"total_cell_count":10}],"canvas_size":[597,400],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.52,"id":"combination_2992","image_path":"images/combination_2992.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2992_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2992_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_2992_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":"combination_2992_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2992_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2992,"target_cell_count":10,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[1,3],[2,2],[2,3],[3,1],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,1],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[3,1],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2],[1,1],[1,2],[2,0],[2,1],[2,2],[2,3],[3,2]],[[0,0],[0,1]]],"total_cell_count":10},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2],[2,2],[3,2]],[[0,0]],[[0,0]]],"total_cell_count":9}],"canvas_size":[581,425],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.58,"id":"combination_2993","image_path":"images/combination_2993.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination_2993_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2993_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination_2993_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":"combination_2993_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2993_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2993,"target_cell_count":10,"target_cells":[[0,1],[0,2],[0,3],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0],[3,0]],[[0,0],[0,1],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[3,0],[3,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0],[1,0],[1,1],[1,2],[2,0],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[1,0],[1,1]]],"total_cell_count":7}],"canvas_size":[586,426],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2994","image_path":"images/combination_2994.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2994_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2994_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination_2994_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":"combination_2994_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2994_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2994,"target_cell_count":8,"target_cells":[[0,0],[1,0],[2,0],[3,0],[3,1],[4,1],[5,1],[5,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,0],[1,1],[2,1],[2,2]],[[0,0],[0,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[2,0],[2,1]],[[0,0],[0,1]]],"total_cell_count":8}],"canvas_size":[572,408],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_2995","image_path":"images/combination_2995.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2995_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2995_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2995_q3","question_text":"Does candidate B have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2995_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2995_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2995,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[1,3],[2,1],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,0],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[1,1],[2,0],[2,1],[3,0]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,0]],[[0,0],[0,1]],[[0,0]]],"total_cell_count":8}],"canvas_size":[562,404],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2996","image_path":"images/combination_2996.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2996_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_2996_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination_2996_q3","question_text":"Does candidate A have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination_2996_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2996_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2996,"target_cell_count":8,"target_cells":[[0,2],[0,3],[1,0],[1,1],[1,2],[2,2],[2,3],[3,2]]}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[1,2],[2,2]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[0,1],[1,0],[2,0],[2,1]]],"total_cell_count":6},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,2],[1,0],[1,1],[1,2],[2,1]],[[0,0]]],"total_cell_count":6},{"choice_label":"D","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[1,1],[2,1]],[[0,0]]],"total_cell_count":5}],"canvas_size":[553,414],"correct_answer_choice":"A","dataset_version":"combination-4.0.0","difficulty_score":0.3,"id":"combination_2997","image_path":"images/combination_2997.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"6","question_id":"combination_2997_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination_2997_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination_2997_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":"combination_2997_q4","question_text":"Which candidate cannot form the target because its combined area has the wrong number of unit cells?","question_type":"wrong_area_choice"},{"answer_format":"yes_no","difficulty_level":5,"ground_truth":"yes","question_id":"combination_2997_q5","question_text":"If one extra unit cell were attached along an edge of the correctly assembled connected target, would the result remain connected? Answer yes or no.","question_type":"extra_cell_connectivity"}],"seed":2997,"target_cell_count":6,"target_cells":[[0,0],[0,1],[1,0],[1,1],[1,2],[2,2]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,0],[2,0]],[[0,0]],[[0,0]]],"total_cell_count":6},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1],[1,0],[1,1],[2,0],[3,0]],[[0,0]],[[0,0]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1],[0,2],[1,0],[1,1],[1,2]],[[0,0],[0,1]]],"total_cell_count":7},{"choice_label":"D","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0],[2,0],[2,1],[3,1]],[[0,0]],[[0,0]]],"total_cell_count":7}],"canvas_size":[575,404],"correct_answer_choice":"B","dataset_version":"combination-4.0.0","difficulty_score":0.415,"id":"combination_2998","image_path":"images/combination_2998.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"7","question_id":"combination_2998_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination_2998_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination_2998_q3","question_text":"Does candidate D have the same total number of unit cells as the target? Answer yes or no.","question_type":"candidate_same_area"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination_2998_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2998_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2998,"target_cell_count":7,"target_cells":[[0,1],[1,0],[1,1],[2,0],[2,1],[2,2],[3,0]]}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1]]],"total_cell_count":7},{"choice_label":"B","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[1,0],[1,1],[2,1],[2,2]]],"total_cell_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[1,0]],[[0,0]],[[0,1],[0,2],[1,0],[1,1],[2,1]]],"total_cell_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0]],[[0,0],[1,0],[1,2],[2,0],[2,1],[2,2],[3,1]]],"total_cell_count":8}],"canvas_size":[593,417],"correct_answer_choice":"C","dataset_version":"combination-4.0.0","difficulty_score":0.47,"id":"combination_2999","image_path":"images/combination_2999.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_2999_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination_2999_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination_2999_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":"combination_2999_q4","question_text":"Which candidate has the wrong total number of unit cells compared with the target?","question_type":"wrong_area_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_2999_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":2999,"target_cell_count":8,"target_cells":[[0,1],[1,1],[1,2],[2,1],[2,2],[3,0],[3,1],[4,1]]}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0],[0,1]],[[0,0],[0,1],[1,0],[1,1]],[[0,0],[1,0]]],"total_cell_count":8},{"choice_label":"B","failure_reason":"wrong_area","is_valid_assembly":false,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2]]],"total_cell_count":7},{"choice_label":"C","failure_reason":"requires_reflection","is_valid_assembly":false,"pieces":[[[0,1],[1,0],[1,1]],[[0,0],[1,0],[1,1],[1,2],[2,2]]],"total_cell_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0],[0,1],[1,1]],[[0,2],[1,0],[1,1],[1,2],[2,0]]],"total_cell_count":8}],"canvas_size":[590,408],"correct_answer_choice":"D","dataset_version":"combination-4.0.0","difficulty_score":0.41,"id":"combination_3000","image_path":"images/combination_3000.png","questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination_3000_q1","question_text":"How many unit cells make up the target shape?","question_type":"target_cell_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination_3000_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation, with no mirroring, to exactly form the target?","question_type":"assembly_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination_3000_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":"combination_3000_q4","question_text":"Which candidate has the correct area but would require flipping (mirroring) its pieces to form the target?","question_type":"requires_reflection_choice"},{"answer_format":"choice","difficulty_level":5,"ground_truth":"connected","question_id":"combination_3000_q5","question_text":"If the topmost, then leftmost, target cell were removed, would the remaining target be connected or disconnected?","question_type":"remove_top_left_cell_connectivity"}],"seed":3000,"target_cell_count":8,"target_cells":[[0,0],[0,1],[1,1],[1,3],[2,1],[2,2],[2,3],[3,1]]}